MCQ
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 :
- ✓$x-y=1$
- B$2 x+y=5$
- C$x+3 y=5$
- D$x+2 y=4$
Mirror image on $y = x \Rightarrow C : x ^{2}=4 y$
$2 x =4 \cdot \frac{ dy }{ dx } \Rightarrow \frac{ dy }{ dx }=\frac{ x }{2}$
$\left.\frac{ dy }{ dx }\right|_{ P (2,1)}=\frac{2}{2}=1$
Equation of tangent at $(2,1)$
$\Rightarrow y-1=1(x-2)$
$\Rightarrow x-y=1$
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