Question

The mirror image of the focus to the parabola $4\left(x+y\right)=y^2$ w.r.t. the directrix is

• A. $\left(0,2\right)$
• B. $\left(2,2\right)$
• C. $\left(-4,2\right)$
• D. $\left(-2,2\right)$

Answer 1

The correct option is D $\left(-2,2\right)$

given, $4(x+y)=y^2$

$4x=y^2-4y$

making perfect square in $(y-2)$

$y(x+1)={(y-2)}^2.....\left(1\right)$

comparing to $y^2=4ax$

$a=1$

shifting origin to $x=1$ , $y=2$

${\left(y\right)}^2=4\left(x\right)$

focus is $(0,2)$ so the image in $x=-1$ i.e., directive is $(-2,2)$