JEE PYQ: Application Of Derivatives Question 3
Question 3 - 2021 (16 Mar Shift 2)
Let C be the locus of the mirror image of a point on the parabola $y^2 = 4x$ with respect to the line $y = x$. Then the equation of tangent to C at $P(2, 1)$ is:
(1) $x - y = 1$
(2) $2x + y = 5$
(3) $x + 3y = 5$
(4) $x + 2y = 4$
Show Answer
Answer: (1)
Solution
Mirror image of $y^2 = 4x$ on $y = x$ gives $C: x^2 = 4y$. At $P(2,1)$: $\frac{dy}{dx} = \frac{x}{2} = 1$. Tangent: $y - 1 = 1(x - 2) \Rightarrow x - y = 1$.
BETA
