Q.
Image or reflection of a curve about a line mirror
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'.
The image of the rectangular hyperbola $x y=9$ in the line $y=3$ is -
Straight Lines
Solution: