Let \( S^{\prime}=0 \) be the image or reflection of the curve \( S=0 \) about line mirror \( L=0 \) Suppose \( P \) be any point on the curve \( S=0 \) and \( Q \) be the image or reflection about the line mirror \( L=0 \), then \( Q \) will lie on \( S^{\prime}=0 \) How to find the image or reflection of a curve?
Let the given curve be \( S: f(x, y)=0 \) and line mirror \( L: a x+b y+c=0 \). We take a point \( P \) on the given curve in parametric form. Suppose \( Q \) be the image or reflection of point \( P \) about line mirror \( L=0 \) which again contains the same parameter. Let \( Q \equiv(\phi(t), \psi(t)) \), where \( t \) is parameter. Now let \( x=\phi(t) \) and \( y=\psi(t) \)
Eliminating \( t \), we get the equation of the reflected curve \( S^{\prime} \).
The image of the parabola \( x^{2}=4 y \) in the line \( x+y=a \) is
(a) \( (x-a)^{2}=4(a-y) \)
(b) \( (y-a)^{2}=4(a-x) \)
(c) \( (x-a)^{2}=4(a+y) \)
(d) \( (y-a)^{2}=4(a+x) \)
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