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The coordinates of the centre of a circle is (-2, 3). If its...

The coordinates of the centre of a circle is (-2, 3). If its area is 25πcm2, find its equation. 

A.

x2+y24x6y12=0

B.

x2+y24x+6y12=0

C.

x2+y2+4x+6y12=0

D.

x2+y2+4x6y12=0

Correct answer is D

Equation of a circle with centre coordinates (a, b) : (xa)2+(yb)2=r2

Area of circle = πr2=25πcm2r2=25

(a, b) = (-2, 3)

Equation: (x - (-2))^{2} + (y - 3)^{2} = 5^{2}

x^{2} + 4x + 4 + y^{2} - 6y + 9 = 25 \implies x^{2} + y^{2} + 4x - 6y + 13 - 25 = 0

= x^{2} + y^{2} + 4x - 6y - 12 = 0