Question

A ray of light moving parallel to $x-$axis gets reflected from the parabolic mirror whose equation is given by $y^2-10y-8x+41=0$ After reflection, the ray must passes through the point

• A. $(4,5)$
• B. $(-4,-5)$
• C. $(-4,5)$
• D. $(4,-5)$

Answer 1

Answer: (A)

$(4,5)$

As $y^2-10y-8x+41=0$
$\Rightarrow {(y-5)}^2=8(x-2)$
$\Rightarrow Y^2=8X=4\left(2\right)X$
Where $Y=y-5,X=x-2$
$\Rightarrow$ focus $(X,Y)=(2,0)$
$\Rightarrow x-2=2,y-5=0$
$\Rightarrow x=4,y=5$
$\therefore$ After reflection, the ray must pass through the focus $(4,5)$
Hence choice (a) is correct answer