{"id":30108,"date":"2024-03-05T10:34:10","date_gmt":"2024-03-05T05:04:10","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=30108"},"modified":"2024-03-06T09:33:26","modified_gmt":"2024-03-06T04:03:26","slug":"ap-inter-1st-year-maths-1b-important-questions-chapter-1","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-inter-1st-year-maths-1b-important-questions-chapter-1\/","title":{"rendered":"AP Inter 1st Year Maths 1B Important Questions Chapter 1 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02"},"content":{"rendered":"

Students get through\u00a0AP Inter 1st Year Maths 1B Important Questions<\/a> Chapter 1 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02 which are most likely to be asked in the exam.<\/p>\n

AP Inter 1st Year Maths 1B Important Questions Chapter 1 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02<\/h2>\n

\u0c38\u0c3e\u0c27\u0c3f\u0c02\u0c1a\u0c3f\u0c28 \u0c38\u0c2e\u0c38\u0c4d\u0c2f\u0c32\u0c41<\/span><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1.
\nXOY \u0c24\u0c32\u0c02\u0c32\u0c4b \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 (-2, 3) \u0c28\u0c41\u0c02\u0c1a\u0c3f \u0c26\u0c42\u0c30\u0c02 5\u0c17\u0c3e \u0c17\u0c32 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 \u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\u0c26\u0c24\u0c4d\u0c24 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41\u0c28\u0c41 A = (-2, 3) \u0c05\u0c28\u0c3f, \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02 \u0c2e\u0c40\u0c26\u0c3f \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41\u0c28\u0c41 P(x, y) \u0c05\u0c28\u0c3f \u0c05\u0c28\u0c41\u0c15\u0c4a\u0c02\u0c26\u0c3e\u0c02.
\n\u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 P, \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02 \u0c2e\u0c40\u0c26 \u0c09\u0c02\u0c21\u0c1f\u0c3e\u0c28\u0c3f\u0c15\u0c3f \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c1a\u0c3e\u0c32\u0c4d\u0c38\u0c3f\u0c28 \u0c1c\u0c4d\u0c2f\u0c3e\u0c2e\u0c3f\u0c24\u0c40\u0c2f \u0c28\u0c3f\u0c2f\u0c2e\u0c02
\nAP = 5 ………….. (1)
\n\u0c08 \u0c28\u0c3f\u0c2f\u0c2e\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c2c\u0c40\u0c1c\u0c40\u0c2f\u0c02\u0c17\u0c3e \u0c35\u0c4d\u0c2f\u0c15\u0c4d\u0c24\u0c40\u0c15\u0c30\u0c3f\u0c38\u0c4d\u0c24\u0c47
\n\\(\\sqrt{(x+2)^2+(y-3)^2}\\) = 5
\n\u0c05\u0c02\u0c1f\u0c47, x2<\/sup> + 4x + 4 + y2<\/sup> – 6y + 9 = 25
\n\u0c05\u0c02\u0c1f\u0c47, x2<\/sup> + y2<\/sup> + 4x – 6y – 12 = 0 ……………….. (2)
\n\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02 (2) \u0c28\u0c41 Q(x1<\/sub>, y1<\/sub>) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c28\u0c41 \u0c15\u0c4a\u0c02\u0c26\u0c3e\u0c02.
\n\u0c05\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 x1<\/sub>2<\/sup> + y1<\/sub>2<\/sup> + 4x1<\/sub> – 6y1<\/sub> – 12 = 0
\n\u0c07\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 A, Q\u0c32 \u0c2e\u0c27\u0c4d\u0c2f\u0c26\u0c42\u0c30\u0c02
\nAQ = \\(\\sqrt{\\left(x_1+2\\right)^2+\\left(y_1-3\\right)^2}\\)
\n\u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 AQ2<\/sup> = x1<\/sub>2<\/sup> + 4x1<\/sub> + 4 + y1<\/sub>2<\/sup> – 6y1<\/sub> + 9
\n= (x1<\/sub>2<\/sup> + y1<\/sub>2<\/sup> + 4x1<\/sub> + 6y1<\/sub> – 12) + 25
\n= 25 ((3) \u0c28\u0c41 \u0c09\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c38\u0c4d\u0c24\u0c47)
\n\u0c15\u0c3e\u0c2c\u0c1f\u0c4d\u0c1f\u0c3f AQ = 5
\n\u0c05\u0c02\u0c1f\u0c47 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 Q(x1<\/sub>, y1<\/sub>) \u0c1c\u0c4d\u0c2f\u0c3e\u0c2e\u0c3f\u0c24\u0c40\u0c2f \u0c28\u0c3f\u0c2f\u0c2e\u0c02 (1) \u0c28\u0c3f \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c28\u0c3f \u0c05\u0c30\u0c4d\u0c25\u0c02.
\n\u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 \u0c15\u0c3e\u0c35\u0c32\u0c38\u0c3f\u0c28 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02
\nx2<\/sup> + y2<\/sup> + 4x – 6y – 12 = 0.<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 2.
\n\u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 A(3, 0) \u0c28\u0c41\u0c02\u0c1a\u0c3f P \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 \u0c26\u0c42\u0c30\u0c02, B(-3, 0) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 \u0c28\u0c41\u0c02\u0c1a\u0c3f P \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 \u0c26\u0c42\u0c30\u0c3e\u0c28\u0c3f\u0c15\u0c3f \u0c30\u0c46\u0c1f\u0c4d\u0c1f\u0c3f\u0c02\u0c2a\u0c41 \u0c05\u0c2f\u0c3f\u0c24\u0c47 P \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\n\u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02 \u0c2e\u0c40\u0c26 P(x, y) \u0c12\u0c15 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c28\u0c41\u0c15\u0c4a\u0c02\u0c26\u0c3e\u0c02.
\n\u0c05\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 P \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c1a\u0c47 \u0c1c\u0c4d\u0c2f\u0c3e\u0c2e\u0c3f\u0c24\u0c40\u0c2f \u0c28\u0c3f\u0c2f\u0c2e\u0c02.
\nPA = 2PB
\n\u0c05\u0c02\u0c1f\u0c47 PA2<\/sup> = 4PB2<\/sup>
\n\u0c05\u0c02\u0c1f\u0c47 (x – 3)2<\/sup> + y2<\/sup> = 4[(x + 3)2<\/sup> + y2<\/sup>]
\n\u0c05\u0c02\u0c1f\u0c47 x2<\/sup> – 6x + 9 + y2<\/sup> = 4[x2<\/sup> + 6x + 9 + y2<\/sup>]
\n\u0c05\u0c02\u0c1f\u0c47 3x2<\/sup> + 3y2<\/sup> + 30x + 27 = 0
\n\u0c05\u0c02\u0c1f\u0c47 x2<\/sup> + y2<\/sup> + 10x + 9 = 0 ………………. (2)
\n\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02 (2) \u0c28\u0c41 Q(x1<\/sub>, y1<\/sub>) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c28\u0c41
\n\u0c15\u0c4a\u0c02\u0c26\u0c3e\u0c02.
\n\u0c05\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 x1<\/sub>2<\/sup> + y1<\/sub>2<\/sup> + 10x1<\/sub> + 9 = 0
\n\u0c07\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 QA2<\/sup> = (x1<\/sub> – 3)2<\/sup> + y1<\/sub>2<\/sup> + y1<\/sub>2<\/sup>
\n= x1<\/sub>2<\/sup> – 6x1<\/sub> + 9 + y1<\/sub>2<\/sup>
\n= 4x1<\/sub>2<\/sup> + 24x1<\/sub> + 36 + 4y1<\/sub>2<\/sup>– 3x1<\/sub>2<\/sup> – 30x1<\/sub> – 27 – 3y1<\/sub>2<\/sup>
\n= 4(x1<\/sub>2<\/sup> + 6x1<\/sub> + 9 + y1<\/sub>2<\/sup>) – 3(x1<\/sub>2<\/sup> + 10x1<\/sub> + 9 + y1<\/sub>2<\/sup>)
\n= 4(x1<\/sub>2<\/sup> + 6x1<\/sub> + 9 + y1<\/sub>2<\/sup>) ((3)\u0c28\u0c41 \u0c09\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c38\u0c4d\u0c24\u0c47)
\n= 4[(x1<\/sub> + 3)2<\/sup> + y1<\/sub>2<\/sup>]
\n= 4 QB2<\/sup>
\n\u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 QA = 2QB. \u0c05\u0c02\u0c1f\u0c47 Q(x1<\/sub>, y1<\/sub>) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 (1) \u0c28\u0c3f \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c3f.
\n\u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 \u0c15\u0c3e\u0c35\u0c32\u0c38\u0c3f\u0c28 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02
\nx2<\/sup> + y2<\/sup> + 10x + 9
\n= 0.<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 3.
\n(4, 0), (0, 4) \u0c32\u0c41 \u0c15\u0c30\u0c4d\u0c23\u0c3e\u0c17\u0c4d\u0c30\u0c3e\u0c32\u0c41\u0c17\u0c3e \u0c17\u0c32 \u0c32\u0c02\u0c2c\u0c15\u0c4b\u0c23 \u0c24\u0c4d\u0c30\u0c3f\u0c2d\u0c41\u0c1c\u0c02 \u0c2e\u0c42\u0c21\u0c4b \u0c36\u0c40\u0c30\u0c4d\u0c37\u0c02 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28:
\nA = (4, 0), B = (0, 4) \u0c05\u0c28\u0c41\u0c15\u0c41\u0c02\u0c26\u0c3e\u0c02.
\nPA, PB \u0c32\u0c41 \u0c32\u0c02\u0c2c\u0c02\u0c17\u0c3e \u0c09\u0c02\u0c21\u0c47\u0c1f\u0c1f\u0c4d\u0c32\u0c41 P(x, y) \u0c28\u0c3f \u0c24\u0c40\u0c38\u0c41\u0c15\u0c4a\u0c02\u0c26\u0c3e\u0c02.
\n\u0c05\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 PA2<\/sup> + PB2<\/sup> = AB2<\/sup> …………… (1)
\nP, A, B \u0c32\u0c41 \u0c38\u0c30\u0c47\u0c16\u0c40\u0c2f\u0c3e\u0c32\u0c41 \u0c15\u0c3e\u0c35\u0c41.
\n(x – 4)2<\/sup> + y2<\/sup> + x2<\/sup> + (y – 4)2<\/sup> = 16 + 16,
\nP \u2260 A, P \u2260 B
\n\u0c32\u0c47\u0c26\u0c3e x2<\/sup> + y2<\/sup> – 4x – 4y = 0,
\n(x, y) \u2260 (4, 0), (x, y) \u2260 (0, 4) ……….. (2)
\nQ(x1<\/sub>, y1<\/sub>) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 (2) \u0c28\u0c41 \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c28\u0c3f, Q \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 A, B \u0c32\u0c15\u0c41 \u0c2d\u0c3f\u0c28\u0c4d\u0c28\u0c2e\u0c48\u0c02\u0c26\u0c28\u0c3f \u0c05\u0c28\u0c41\u0c15\u0c4a\u0c02\u0c26\u0c3e\u0c02.
\n\u0c05\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 x1<\/sub>2<\/sup> + y1<\/sub>2<\/sup> – 4x1<\/sub> – 4y1<\/sub> = 0,
\n(x1<\/sub>, y1<\/sub>) \u2260 (4, 0), (x1<\/sub>, y1<\/sub>) \u2260 (0, 4) …………. (3)
\n\u0c07\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 QA2<\/sup> + QB2<\/sup>
\n= (x1<\/sub> – 4)2<\/sup> + y1<\/sub>2<\/sup> + x1<\/sub>2<\/sup> + (y1<\/sub> – 4)2<\/sup>
\n= x1<\/sub>2<\/sup> – 8x1<\/sub> + 16 + y1<\/sub>2<\/sup> + x1<\/sub>2<\/sup> + y1<\/sub>2<\/sup> – 8y1<\/sub> + 16
\n= 2(x1<\/sub>2<\/sup> + y1<\/sub>2<\/sup> – 4x1<\/sub> – 4y1<\/sub>) + 32
\n= 32 ((3)\u0c28\u0c41 \u0c09\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c38\u0c4d\u0c24\u0c47)
\n= AB2<\/sup>
\n\u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 QA2<\/sup> + QB2<\/sup> = AB2<\/sup>, Q \u2260 A, Q \u2260 B.
\n\u0c05\u0c02\u0c1f\u0c47 Q(x1<\/sub>, y) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 (1)\u0c28\u0c3f \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c3f. \u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 (2) \u0c15\u0c3e\u0c35\u0c32\u0c38\u0c3f\u0c28 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02. \u0c07\u0c26\u0c3f A, B\u0c32\u0c41 \u0c2e\u0c3f\u0c28\u0c39\u0c3e, \\(\\overline{\\mathrm{AB}}\\) \u0c28\u0c3f \u0c35\u0c4d\u0c2f\u0c3e\u0c38\u0c02\u0c17\u0c3e \u0c17\u0c32 \u0c35\u0c43\u0c24\u0c4d\u0c24\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c38\u0c42\u0c1a\u0c3f\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c3f.<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 4.
\nA(5, \u22124), B (7, 6) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41\u0c32 \u0c28\u0c41\u0c02\u0c1a\u0c3f P \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 \u0c26\u0c42\u0c30\u0c3e\u0c32 \u0c28\u0c3f\u0c37\u0c4d\u0c2a\u0c24\u0c4d\u0c24\u0c3f 2 : 3 \u0c05\u0c2f\u0c3f\u0c24\u0c47, P \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c3e\u0c28\u0c4d\u0c28\u0c3f \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. [Mar. ’14]
\n\u0c38\u0c3e\u0c27\u0c28:
\n\u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02 \u0c2e\u0c40\u0c26\u0c3f \u0c12\u0c15 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41\u0c28\u0c41 P(x, y) \u0c05\u0c28\u0c41\u0c15\u0c4a\u0c02\u0c26\u0c3e\u0c02.
\nP \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c1a\u0c47 \u0c1c\u0c4d\u0c2f\u0c3e\u0c2e\u0c3f\u0c24\u0c40\u0c2f \u0c28\u0c3f\u0c2f\u0c2e\u0c02 \\(\\frac{\\mathrm{AP}}{\\mathrm{PB}}=\\frac{2}{3}\\)
\n\u0c05\u0c02\u0c1f\u0c47 3AP = 2PB
\n\u0c05\u0c02\u0c1f\u0c47 AP2<\/sup> = 4PB2<\/sup>
\n\u0c05\u0c02\u0c1f\u0c47 9[(x – 5)2<\/sup> + (y + 4)2<\/sup>] = 4[(x – 7)2<\/sup> + (y – 6)2<\/sup>]
\n\u0c05\u0c02\u0c1f\u0c47 9[x2<\/sup> + 25 – 10x + y2<\/sup> + 16 + 8y] = 4[x2<\/sup> + 49 – 14x + y2<\/sup> + 36 – 12y]
\n\u0c05\u0c02\u0c1f\u0c47 5x2<\/sup> + 5y2<\/sup> – 34x + 120y + 29 = 0
\nQ(x1<\/sub>, y1<\/sub>) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 (2) \u0c28\u0c41 \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c28\u0c41\u0c15\u0c4a\u0c02\u0c26\u0c3e\u0c02.
\n\u0c05\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 51<\/sub>x + 5y1<\/sub> – 34x1<\/sub> + 120y1<\/sub> + 29 = 0
\n\u0c07\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41
\n9AQ2 = 9[x1<\/sub>2<\/sup> + 25 \u2212 10x1<\/sub> + y1<\/sub>2<\/sup> + 16 + 8y1<\/sub>]
\n= 5x1<\/sub>2<\/sup> + 5y1<\/sub>2<\/sup> \u2212 34x1<\/sub> + 120y1<\/sub> + 29 + 4x1<\/sub>2<\/sup> + 4y1<\/sub>2<\/sup> – 56x1<\/sub> – 48y1<\/sub> + 340]
\n= 4[x1<\/sub>2<\/sup> + y1<\/sub>2<\/sup> – 14x1<\/sub> – 12y1<\/sub> +49 + 36] ((3)\u0c28\u0c41 \u0c09\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c38\u0c4d\u0c24\u0c47)
\n= 4[(x1<\/sub> – 7)2<\/sup> + (y1<\/sub> – 6)2<\/sup>]
\n= 4QB2<\/sup>
\n\u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 3AQ = 2QB.
\n\u0c05\u0c02\u0c1f\u0c47 Q(x1<\/sub>, y1<\/sub>) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 (1)\u0c28\u0c3f \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c3f. \u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 \u0c15\u0c3e\u0c35\u0c32\u0c38\u0c3f\u0c28 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c2e\u0c41
\n5(x2<\/sup> + y2<\/sup>) – 34x + 120y + 29 = 0.<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 5.
\nA(2, 3), B(-3, 4) \u0c32\u0c41 \u0c26\u0c24\u0c4d\u0c24 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41\u0c32\u0c41. \u0c24\u0c4d\u0c30\u0c3f\u0c2d\u0c41\u0c1c\u0c02 PAB \u0c35\u0c48\u0c36\u0c3e\u0c32\u0c4d\u0c2f\u0c02 8.5 \u0c09\u0c02\u0c21\u0c47\u0c1f\u0c1f\u0c4d\u0c32\u0c41\u0c17\u0c3e P \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. [Mar. ’11]
\n\u0c38\u0c3e\u0c27\u0c28:
\n\u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02 \u0c2e\u0c40\u0c26\u0c3f \u0c12\u0c15 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41\u0c28\u0c41 P(x, y) \u0c05\u0c28\u0c41\u0c15\u0c41\u0c02\u0c26\u0c3e\u0c02.
\nP\u0c28\u0c3f \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c1a\u0c47 \u0c1c\u0c4d\u0c2f\u0c3e\u0c2e\u0c3f\u0c24\u0c40\u0c2f \u0c28\u0c3f\u0c2f\u0c2e\u0c02
\n\u2206PAB \u0c35\u0c48\u0c36\u0c3e\u0c32\u0c4d\u0c2f\u0c02 = 8.5 ………………. (1)
\n\u0c05\u0c02\u0c1f\u0c47
\n\\(\\frac{1}{2}\\) |x(3 – 4) + 2(4 – y) – 3 (y – 3)| = 8.5
\n\u0c05\u0c02\u0c1f\u0c47 |-x + 8 – 2y – 3y + 9| = 17
\n\u0c05\u0c02\u0c1f\u0c47 |-x – 5y + 17| = 17
\n\u0c05\u0c02\u0c1f\u0c47 -x \u2212 5y + 17 = 17 \u0c32\u0c47\u0c26\u0c3e
\n-x – 5y + 17 = -17
\n\u0c05\u0c02\u0c1f\u0c47 x + 5y = 0 \u0c32\u0c47\u0c26\u0c3e x + 5y = 34
\n\u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 (x + 5y) (x + 5y – 34) = 0
\n\u0c05\u0c02\u0c1f\u0c47 x2<\/sup> + 10xy + 25y2<\/sup> – 34x – 170y = 0 …………. (2)
\nQ(x1<\/sub>, y1<\/sub>) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 (2)\u0c28\u0c3f \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c28\u0c41\u0c15\u0c4a\u0c02\u0c26\u0c3e\u0c02.
\n\u0c05\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 x1<\/sub> + 5y1<\/sub> = 0 \u0c32\u0c47\u0c26\u0c3e
\nx1<\/sub> + 5y1<\/sub> = 34 ……………. (3)
\n\u0c07\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 \u2206QAB \u0c35\u0c48\u0c36\u0c3e\u0c32\u0c4d\u0c2f\u0c02
\n= \\(\\frac{1}{2}\\)|(x1<\/sub> (3 – 4) + 2(4 – y1<\/sub>) – 3(y1<\/sub> – 3)|
\n= \\(\\frac{1}{2}\\) |-x1<\/sub> + 8 – 2y1<\/sub> – 3y1<\/sub> + 9|
\n= \\(\\frac{1}{2}\\) |-x1<\/sub> – 5y1<\/sub> + 17|
\n= \\(\\frac{17}{2}\\) = 8.5 ((3)\u0c28\u0c41 \u0c09\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c38\u0c4d\u0c24\u0c47)
\n\u0c05\u0c02\u0c1f\u0c47 Q(x1<\/sub>, y1<\/sub>) \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 (1)\u0c28\u0c3f \u0c24\u0c43\u0c2a\u0c4d\u0c24\u0c3f\u0c2a\u0c30\u0c41\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c3f.
\n\u0c05\u0c02\u0c26\u0c41\u0c35\u0c32\u0c4d\u0c32 \u0c15\u0c3e\u0c35\u0c32\u0c38\u0c3f\u0c28 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02
\n(x + 5y) (x + 5y – 34) = 0
\nx2<\/sup> + 10xy + 25y2<\/sup> – 34x – 170y = 0<\/p>\n","protected":false},"excerpt":{"rendered":"

Students get through\u00a0AP Inter 1st Year Maths 1B Important Questions Chapter 1 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02 which are most likely to be asked in the exam. AP Inter 1st Year Maths 1B Important Questions Chapter 1 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c2a\u0c25\u0c02 \u0c38\u0c3e\u0c27\u0c3f\u0c02\u0c1a\u0c3f\u0c28 \u0c38\u0c2e\u0c38\u0c4d\u0c2f\u0c32\u0c41 \u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1. XOY \u0c24\u0c32\u0c02\u0c32\u0c4b \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 (-2, 3) \u0c28\u0c41\u0c02\u0c1a\u0c3f \u0c26\u0c42\u0c30\u0c02 5\u0c17\u0c3e \u0c17\u0c32 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41 \u0c2a\u0c25 \u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. \u0c38\u0c3e\u0c27\u0c28: \u0c26\u0c24\u0c4d\u0c24 \u0c2c\u0c3f\u0c02\u0c26\u0c41\u0c35\u0c41\u0c28\u0c41 A … Read more<\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[14],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/30108"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=30108"}],"version-history":[{"count":3,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/30108\/revisions"}],"predecessor-version":[{"id":30119,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/30108\/revisions\/30119"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=30108"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=30108"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=30108"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}