JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
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 & Solution
Correct Answer
(A) \(x-y=1\)
Step-by-step Solution
Detailed explanation
Given \(y^{2}=4 x\) 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 \((2,1)\) \(\Rightarrow y-1=1(x-2)\)…
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