The coordinates of the centre of a circle is (-2, 3). If its area is \(25\pi cm^{2}\), find its equation.
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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 = \(\pi r^{2} = 25\pi cm^{2} \implies r^{2} = 25 \)
\(\therefore r = 5cm\)
(a, b) = (-2, 3)
Equation: \((x - (-2))^{2} + (y - 3)^{2} = 5^{2}\)
\(x^{2} + 4x + 4 + y^{2} - 6y + 9 = 25 \implies x^{2} + y^{2} + 4x - 6y + 13 - 25 = 0\)
= \(x^{2} + y^{2} + 4x - 6y - 12 = 0\)
Equation of a circle with centre coordinates (a, b) : \((x - a)^{2} + (y - b)^{2} = r^{2}\)
Area of circle = \(\pi r^{2} = 25\pi cm^{2} \implies r^{2} = 25 \)
\(\therefore r = 5cm\)
(a, b) = (-2, 3)
Equation: \((x - (-2))^{2} + (y - 3)^{2} = 5^{2}\)
\(x^{2} + 4x + 4 + y^{2} - 6y + 9 = 25 \implies x^{2} + y^{2} + 4x - 6y + 13 - 25 = 0\)
= \(x^{2} + y^{2} + 4x - 6y - 12 = 0\)