JEE Main 2021MathematicsParabolaEasyNumerical

JEE Main 2021 — Parabola Question with Solution

JEE Main 2021 (31 Aug Shift 2)

Question

A tangent line L is drawn at the point 2, -4 on the parabola y2=8x. If the line L is also tangent to the circle x2+y2=a, then a is equal to                       .

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

Given, Parabola y2=8x  and circle x2+y2=a2

 Parabola y2=8x at point 2,-4

Differentiating w .r. t.  x''

2ydydx=8

dydx=4y

dydx2,-4=-1

Equation of tangent

y-y1=dydxx-x1

y+4=-1x-2

x+y+2=0

Line L is also tangent to the circle x2+y2=a2

So, OA=a   at 0,0

1×0+1×0+22=a

2=a

⇒a=2

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About this question

This is a previous-year question from JEE Main 2021, covering the Parabola 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.