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A ray of light moving parallel to the $x$-axis gets reflected from a parabolic mirror whose equation is $(y-2)^2=4(x+1)$. After reflection, the ray must pass through the point
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Verified Answer
The correct answer is:
$(0,2)$
Given parabola is $(y-2)^2=4(x+1)$
$\Rightarrow \mathrm{Y}^2=4 \mathrm{aX}$ where $\mathrm{X}=\mathrm{x}+1, \mathrm{Y}=\mathrm{Y}-2, \mathrm{a}=1$
We know focus of parabola $Y^2=4 \mathrm{aX}$ is $(\mathrm{X}=-\mathrm{a}, \mathrm{Y}=0)$
$\Rightarrow(\mathrm{x}+1=1, \mathrm{y}-2=0)=(0, 2)$
Thus focus of the given parabola is $(0,2)$
We know every reflected ray from parabolic mirror passes through its focus.
Hence option '3' is correct choice.
$\Rightarrow \mathrm{Y}^2=4 \mathrm{aX}$ where $\mathrm{X}=\mathrm{x}+1, \mathrm{Y}=\mathrm{Y}-2, \mathrm{a}=1$
We know focus of parabola $Y^2=4 \mathrm{aX}$ is $(\mathrm{X}=-\mathrm{a}, \mathrm{Y}=0)$
$\Rightarrow(\mathrm{x}+1=1, \mathrm{y}-2=0)=(0, 2)$
Thus focus of the given parabola is $(0,2)$
We know every reflected ray from parabolic mirror passes through its focus.
Hence option '3' is correct choice.
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