CircleHard

Question

Two parabolas have the same focus. If their directrices are the x-axis & the y-axis respectively, then the slope of their common chord is -

Options

A.1
B.-1
C.4/3
D.3/4

Solution

   
P1 ≡ (x - a)2 = 4.
⇒   x2 - 2ax + a2 - 2yb + b2 = 0
Similarly
P2 ≡  y2 - 2ax - 2by + a2 + b2 = 0
Common chord is P1 - P2 = 0
⇒   x2 - y2 = 0    ⇒  (x + y) (x -y) = 0
slope will be 1, -1

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