Question

Let the curve C be the mirror image of the parabola y2 = 4x with respect to the line x + y + 4 = 0. If A and B are the points of intersection of C with the line y = –5, then the distance between A and B is

• A. 4

Answer 1

The correct option is A 4

Equation of AA' is
$y+5=1(x-\alpha )$
$\Rightarrow y=x-\alpha -5$
$y-x=-\alpha -5$.... (i)
Also,
$x+y=-4$

$y=\frac{-\alpha -9}{2},2x=\alpha +1$

$\Rightarrow x=\frac{\alpha +1}{2}$

$M\equiv (\frac{\alpha +1}{2},\frac{\alpha -9}{2})$

$A^{\prime }=(1,-\alpha -4)$
$A^{\prime }$ lies on parabola
Now,
${\alpha }^2+16+8\alpha =4$
$\Rightarrow$ ${\alpha }^2+8\alpha +12=0$
$\Rightarrow \alpha =-2,-6$
AB = distance = 4 units