Question

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 $L$ : $ax+by+c=0$. 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 $Q\equiv (\varphi (t),\psi (t))$ where $t$ is parameter. Now let $x=\varphi (t)$ and $y=\psi (t)$
Eliminating t, we get the equation of the reflected curve S'.
The image of the rectangular hyperbola $xy=9$ in the line $y=3$ is -

• A. $xy+9=0$
• B. $xy-6x+9=0$
• C. $xy+6x-9=0$
• D. $xy+6x+9=0$

Answer 1

Answer: (B)

Correct answer is (b) $xy-6x+9=0$