Answer:

The general form of the equation of a circle is (x – h)² + (y – k)² = r²

(h, k) is the centre of the circle. r is the radius of the circle.

The centre lies on Y – axis,

∴ it’s X – coordinate = 0, h = 0

(0, k) is the centre of the circle.

Substituting the given values in general form of the equation of a circle,

(3 – 0)² + (2 – k)² = 5²

(3)² + (2 – k)² = 25

9 + (2 – k)² = 25

(2 – k)² = 25 – 9 => 16

Taking square root on both sides,

2 – k = ±4

2 – k = 4 & 2 – k = – 4

k = 2 – 4 & k = 2 + 4

k = – 2 & k = 6

The equation of circle,

(i) When k = – 2 is x² + (y + 2)² = 25

(ii) When k = 6 is x² + (y – 6)² = 25