Question

If one of the diameters of the circle x² + y² – 2x – 6y + 6 = 0 is a chord to the circle with centre (2, 1), then the radius of the circle is ………

(a) 3

(b) √3

(c) 2

(d) √2   

Answer 1

The correct option (a) 3   

Explanation:

Circle is x² + y² – 2x – 6y + 6 = 0

∴ Centre of circle is (1, 3)

Radius = √(1 + 9 – 6) = 2

Required equation of circle is

(x – 2)² + (y – 1)² = r² .....(1)

Common chord of (1) and circle

x² + y² – 2x – 6y + 6 = 0 is – 2x + 4y + 5 – r² – 6 = 0

given: it is diameter of circle (2)

∴ – 2(1) + 4(3) + 5 – r² – 6 = 0

∴          r² = 9

∴          r = 3

∴ Radius of required circle is 3.