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AP EAMCET202023 Sep 2020Morning ShiftMathematicsStraight LinesActual

Two points A and B with co-ordinates ( 1 , 1 ) and ( - 2 , 3 ) are given respectively. Then, the locus of a point P so that the area of Δ P A B is 9 sq.units is given by _____

Options

  1. A2 x + 3 y + 13 = 0   &   2 x + 3 y - 23 = 0
  2. B2 x + 3 y + 23 = 0   &   2 x + 3 y - 13 = 0
  3. C2 x + 3 y - 13 = 0   &   2 x - 3 y + 23 = 0
  4. D2 x - 3 y + 23 = 0   &   2 x + 3 y + 13 = 0

Correct answer

A. 2 x + 3 y + 13 = 0   &   2 x + 3 y - 23 = 0

Step-by-step solution

Given, A ( 1 , 1 )   a n d   B ( - 2 , 3 ) L e t   P ( x , y ) be the point as per given condition A ( △ P A B ) = 9 We know that, if 3 points are given then the area of triangle is given by - 1 2 x y 1 1 1 1 - 2 3 1 = 9 ⇒ x ( 1 - 3 ) - y ( 1 + 2 ) + 1 ( 3 + 2 ) = 9 × 2 ⇒ x ( - 2 ) - 3 y + 5 = 18 ⇒ - 2 x - 3 y + 5 = ± 18 ⇒ - 2 x - 3 y = ± 18 - 5 ⇒ - 2 x - 3 y = 18 - 5   a n d   - 2 x - 3 y = - 18 - 5 ⇒ - 2 x - 3 y = 13   a n d &#

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