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MHT CET2017MathematicsPair of Lines

O ( 0 , 0 ) , A ( 1 , 2 ) , B ( 3 , 4 ) are the vertices of ∆ O A B . The joint equation of the altitude and median drawn from O is

Options

  1. Ax 2 + 7 x y - y 2 = 0
  2. Bx 2 + 7 x y + y 2 = 0
  3. C3 x 2 - x y - 2 y 2 = 0
  4. D3 x 2 + x y - 2 y 2 = 0

Correct answer

D. 3 x 2 + x y - 2 y 2 = 0

Step-by-step solution

O P → A l t i t u d e O D → M e d i a n Equation of median O D = y = m x ⇒ 3 = 2 m ⇒ m = 3 2 ∴ y = 3 2 x ⇒ 3 x - 2 y = 0 Slope of A B = 2 2 = 1 ⇒ s l o p e o f O P = - 1 Equation of O P ⇒ y = - x ⇒ x + y = 0 Joint equation of O P a n d O D ⇒ ( x + y ) ( 3 x - 2 y ) = 0 ⇒ 3 x 2 + x y - 2 y 2 = 0

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