The coordinates of the centre of a circle is (-2, 3). If its area is (25pi cm^{2}), find its equation.
-
A.
(x^{2} + y^{2} – 4x – 6y – 12 = 0) -
B.
(x^{2} + y^{2} – 4x + 6y – 12 = 0) -
C.
(x^{2} + y^{2} + 4x + 6y – 12 = 0) -
D.
(x^{2} + y^{2} + 4x – 6y – 12 = 0)
Correct Answer: Option D
Explanation
Equation of a circle with centre coordinates (a, b) : ((x – a)^{2} + (y – b)^{2} = r^{2})
Area of circle = (pi r^{2} = 25pi cm^{2} implies r^{2} = 25 )
(therefore r = 5cm)
(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)