A ray of light moving parallel to the x-axis | vedclass

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(C) The given equation of the parabola is $(y - 2)^2 = 4(x + 1)$.Comparing this with the standard form $(y - k)^2 = 4a(x - h)$,we get the vertex $(h,

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$(0, 2)$

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(C) The given equation of the parabola is $(y - 2)^2 = 4(x + 1)$.Comparing this with the standard form $(y - k)^2 = 4a(x - h)$,we get the vertex $(h, k) = (-1, 2)$ and $4a = 4$,which implies $a = 1$.The axis of the parabola is $y - 2 = 0$,which is parallel to the $x$-axis.According to the optical property of a parabola,any ray of light moving parallel to the axis of the parabola passes through its focus after reflection.The focus of the parabola is given by $(h + a, k) = (-1 + 1, 2) = (0, 2)$.Therefore,the reflected ray must pass through the point $(0, 2)$.

$A$ 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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