Q. 9

# Find the equation

The general form of the equation of a circle is:

(x - h)2 + (y - k)2 = r2

Where, (h, k) is the centre of the circle.

r is the radius of the circle.

Since, centre lies on Y - axis, it’s X - coordinate = 0, i.e.h = 0

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

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

(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 we get,

2 - k = ±4

2 - k = 4 & 2 - k = - 4

k = 2 - 4 & k = 2 + 4

k = - 2 & k = 6

Equation of circle when k = - 2 is:

x2 + (y + 2)2 = 25

Equation of circle when k = 6 is:

x2 + (y - 6)2 = 25

Ans: Equation of circle when k = - 2 is:

x2 + (y + 2)2 = 25

Equation of circle when k = 6 is:

x2 + (y - 6)2 = 25

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