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Maths Circle and System of Circles Equations of Circle, Geometrical Problems Regarding Circle, Centre of The Circle, Radius of The Circle Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference 10 π , then the equation of the circle is-

x 2 + y 2 – 2x + 2y – 23 = 0

x 2 + y 2 – 2x – 2y – 23 = 0

x 2 + y 2 + 2x + 2y – 23 = 0

x 2 + y 2 + 2x – 2y – 23 = 0

Text Solution

Verified by Experts

The correct answer is:

Solving 2x + 3y + 1 = 0 and 3x – y –4 = 0

we get centre (1, –1)

As circumference = 10 π

2π r = 10 π ⇒ r = 5

required equation of circle is

(x – 1) 2 + (y + 1) 2 = 5 2

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