Question

A ray of light moving parallel to the x-axis gets reflected from a parabolic mirror whose equation is $y^2+10y-4x+17=0$. After reflection, the ray must pass through the point

• A. $(-2,-5)$
• B. $(-1,-5)$
• C. $(-3,-5)$
• D. $(-4,-5)$

Answer 1

The correct option is B $(-1,-5)$

Given parabola is, $y^2+10y-4x+17=0$
$\Rightarrow y^2+10y+25=4x+8$
$\Rightarrow (y+5{)}^2=4(x+2)$
Thus focus of the parabola is $(-1,-5)$
And we know ray after reflection from parabola passes through its focus.
Hence, reflected ray passes through $(-1,-5)$