Find the equation of a circle with centre (-3, -8) and radius (4sqrt{6}).
-
A.
(x^{2} – y^{2} – 6x + 16y + 23 = 0) -
B.
(x^{2} + y^{2} + 6x + 16y – 23 = 0) -
C.
(x^{2} + y^{2} + 6x – 16y + 23 = 0) -
D.
(x^{2} + y^{2} – 6x + 16y + 23 = 0)
Correct Answer: Option B
Explanation
Equation of a circle: ((x – a)^{2} + (y – b)^{2} = r^{2})
where (a, b) and r are the coordinates of the centre and radius respectively.
Given : ((a, b) = (-3, -8); r = 4sqrt{6})
((x – (-3))^{2} + (y – (-8))^{2} = (4sqrt{6})^{2})
(x^{2} + 6x + 9 + y^{2} + 16y + 64 = 96)
(x^{2} + y^{2} + 6x + 16y + 9 + 64 – 96 = 0)
(implies x^{2} + y^{2} + 6x + 16y – 23 = 0)