JEE Main 2020MathematicsApplication of DerivativesMediumNumerical

JEE Main 2020 — Application of Derivatives Question with Solution

JEE Main 2020 (03 Sep Shift 2)

Question

If the tangent to the curve y=ex at a point c, ec and the normal to the parabola y2=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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Show full solutionCorrect answer: 4
Correct answer
4

Step-by-step explanation

For the parabola y2=4x, a=1

Let at2, 2at=1, 2

⇒t=1

So, equation of normal is tx+y=2at+at3.

⇒x+y=3 intersects x-axis at 3, 0

Given curve y=ex⇒dydx=ex

So, equation of tangent to the curve at c, ec is y-ec=ecx-c.

At 3, 0⇒0-ec=ec3-c⇒c=4.

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About this question

This is a previous-year question from JEE Main 2020, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.