Double ordinate `A B` of the parabola `y^2=4a x` subtends an angle `pi/2` at the focus of the parabola. Then the tangents drawn to the parabola at `Aa n dB` will intersect at `(-4a ,0)` (b) `(-2a ,0)` `(-3a ,0)` (d) none of these

Options

A. (-4a,0)
B. (-2a,0)
C. (-3a,0)
D. none of these

Answer

A

Explanation

(1) Let `A-=(at^(2),2at),B-=(at^(2),-2at)`. Then
`m_(OA)=(2)/(t),m_(OB)=(-2)/(t)`
Thus, `((2)/(t))((-2)/(t))=-1`
`or" "t^(2)=4`
Thus, the tangents will intersect at (-4a,0).