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Highly selective Backlog Qs for JEE MainMathematicsStraight Lines

A straight line passing through a fixed point 3 ,   5 intersects the coordinate axes at two points A and B . If the locus of C x ,   y which forms a rectangle with the points A ,   O (origin) and B is a x + 2 h x y + b y = 0 then a + b + h =

Options

  1. A17 2
  2. B7
  3. C15 2
  4. D10

Correct answer

C. 15 2

Step-by-step solution

A Straight line passing through a fixed point 3 , 5 and intersects coordinate axis at point A   and B . Let coordinates of A p , 0 and B 0 , q ∴   Intercept form of line is x p + y q = 1 Here, point 3 , 5   will satisfy the line. ⇒   3 p + 5 q = 1 Here, coordinate of point are C ( x , y ) = ( p , q ) Hence, to find locus of C substitute p = x   &   q = y in the above equation. ⇒   3 x + 5 y = 1   ⇒   5 x + 3 y - x y = 0 Now compare a x + b y +

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