JEE Main 2023MathematicsCircleEasyMCQ

JEE Main 2023 — Circle Question with Solution

JEE Main 2023 (30 Jan Shift 1)

Question

Let y=x+2, 4y=3x+6 and 3y=4x+1 be three tangent lines to the circle (x-h)2+(y-k)2=r2. Then h+k is equal to :

Choose an option

Show full solutionCorrect option: A
Correct answer
A5

Step-by-step explanation

Lines y=x+2, 4y=3x+6 and 3y=4x+1 are tangents to the circle (x-h)2+(y-k)2=r2.

Centre of the circle is h,k.

Equation of bisector of lines 4y=3x+6, 3y=4x+1 is:

4x-3y+15=±3x-4y+65

⇒4x-3y+1=±3x-4y+6

Taking positive sign, we get

4x-3y+1=3x-4y+6

⇒x+y=5

Since, centre h,k lies on the bisector, therefore

h+k=5

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About this question

This is a previous-year question from JEE Main 2023, 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.