Question

Let $C$ be the locus of the mirror image of a point on the parabola $y ^{2}=4 x$ with respect to the line $y = x$. Then the equation of tangent to $C$ at $P (2,1)$ is:

• A. x - y = 1
• B. 2 x + y = 5
• C. x + 3 y = 5
• D. x + 2 y = 4

Answer 1

Answer: (A)

Given $y ^{2}=4 x$
Mirror image on $y = x $
$\Rightarrow C : x ^{2}=4 y$
$2 x =4 \cdot \frac{ d y }{ dx } \Rightarrow \frac{ dy }{ dx }=\frac{ x }{2}$
$\left.\frac{ dy }{ dx }\right|_{ P (2,1)}=\frac{2}{2}=1$
Equation of tangent at $(2,1)$
$\Rightarrow y -1=1( x -2)$
$\Rightarrow x-y=1$