Find the equation of a circle with centre (2, -3) and radius 2 units.
Answer Details
The equation of a circle with center (h,k) and radius r is given by the formula:
$$(x-h)^2 + (y-k)^2 = r^2$$
In this case, the center of the circle is (2,-3) and the radius is 2 units. Therefore, we have:
$$(x-2)^2 + (y+3)^2 = 2^2$$
Expanding the left-hand side, we get:
$$x^2 - 4x + 4 + y^2 + 6y + 9 = 4$$
Simplifying this equation, we get:
$$x^2 + y^2 - 4x + 6y + 9 = 0$$
Therefore, the equation of the circle is (A) \(x^{2} + y^{2} - 4x + 6y + 9 = 0\).