JEE Main 2021MathematicsCircleMediumMCQ

JEE Main 2021 — Circle Question with Solution

JEE Main 2021 (16 Mar Shift 2)

Question

Let the lengths of intercepts on x -axis and y -axis made by the circle x2+y2+ax+2ay+c=0, a<0 be 22 and 25, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x+2y=0, is equal to :

Choose an option

Show full solutionCorrect option: C
Correct answer
C6

Step-by-step explanation

x2+y2+ax+2ay+c=0

2g2-c=2a24-c=22

⇒ a24-c=2 ...1

2f2-c=2a2-c=25

⇒a2-c=5 ...2

1 & 2

3a24=3⇒a=-2 a<0

∴  c=-1

Circle ⇒x2+y2-2x-4y-1=0

⇒x-12+y-22=6

Given x+2y=0⇒m=-12

mtangent=2

Equation of tangent ⇒y-2=2x-1±61+4

⇒2x-y±30=0

Perpendicular distance from 0,0=±304+1=6

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About this question

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