Find the equation of a circle with centre (2, -3) and radius 2 units.
-
A.
(x^{2} + y^{2} – 4x + 6y + 9 = 0) -
B.
(x^{2} + y^{2} + 4x – 6y – 9 = 0) -
C.
(x^{2} + y^{2} + 4x + 6y – 9 = 0) -
D.
(x^{2} + y^{2} + 4x – 6y + 9 = 0)
Correct Answer: Option A
Explanation
The equation of a circle with centre coordinate (a, b) and radius r is :
((x – a)^{2} + (y – b)^{2} = r^{2})
Given centre = (2, -3) and radius r = 2 units
Equation = ((x – 2)^{2} + (y – (-3))^{2} = 2^{2})
(x^{2} – 4x + 4 + y^{2} + 6y + 9 = 4)
(x^{2} + y^{2} – 4x + 6y + 4 + 9 – 4 = 0 implies x^{2} + y^{2} – 4x + 6y + 9 = 0)