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Question: Answered & Verified by Expert
A ray of light moving parallel to $\mathrm{x}$-axis gets reflected from the parabolic mirror whose equation is given by $y^2-10 y-8 x+41=0$ After reflection, the ray must passes through the point
MathematicsParabolaJEE Main
Options:
  • A $(-4,-5)$
  • B $(-4,5)$
  • C $(4,5)$
  • D $(4,-5)$
Solution:
2578 Upvotes Verified Answer
The correct answer is: $(4,5)$
As $y^2-10 y-8 x+41=0$
$\begin{aligned} & \Rightarrow(\mathrm{y}-5)^2=8(\mathrm{x}-2) \\ & \Rightarrow \mathrm{Y}^2=8 \mathrm{X}=4(2) \mathrm{X}\end{aligned}$
Where $Y=y-5, X=x-2$
$\Rightarrow x-2=2, y-5=0$
$\Rightarrow x-2=2, y-5=0$
$\Rightarrow x=4, y=5$
$\therefore$ After reflection, the ray must pass through the focus $(4,5)$ Hence choice (3) is correct answer

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