Equation of a circle with centre C(h, k) such that h 2 –3h …

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

Equation of a circle with centre C(h, k) such that h 2 –3h + 2 = 0 and k 2 –5k + 6 = 0 having radius 4 is

x 2 + y 2 –2x –4y –11 = 0

x 2 + y 2 –2x –6y – 6 = 0

x 2 + y 2 –4x –4y – 8 = 0

x 2 + y 2 –4x –6y –3 = 0

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The correct answer is:

CHECK THE SOLUTION.

(a, b, c, d)

h 2 –3h + 2 = 0 ⇒ h = 1, 2

k 2 –5k + 6 = 0 ⇒ k = 2, 3

∴ (h, k) ≡ (1, 2), (1, 3), (2, 2) or (2, 3)

∴ Circles, centered at (h, k) and radius = 4, are given by

(x – 1) 2 + (y – 2) 2 = 16, (x – 1) 2 + (y – 3) 2 = 16

(x – 2) 2 + (y – 2) 2 = 16, (x – 2) 2 + (y – 3) 2 = 16

∴ , , and are correct.

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