JEE PYQ: Application Of Derivatives Question 33
Question 33 - 2020 (03 Sep Shift 2)
If the tangent to the curve $y = e^x$ at a point $(c, e^c)$ and the normal to the parabola $y^2 = 4x$ at the point $(1, 2)$ intersect at the same point on the $x$-axis, then the value of $c$ is
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Answer: 4
Solution
Normal to $y^2 = 4x$ at $(1,2)$: $x + y = 3$, meets $x$-axis at $(3,0)$. Tangent to $y = e^x$ at $(c, e^c)$: $y - e^c = e^c(x-c)$. At $y=0$: $x = c - 1$. So $c - 1 = 3 \Rightarrow c = 4$.
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