Question

The circle below is centered at the point (2, -3), and the length of its radius is 2. What is the equation of the circle in standard form?

a) (x - 2)^2 + (y + 3)^2 = 4

b) (x + 2)^2 + (y - 3)^2 = 4

c) (x - 2)^2 + (y + 3)^2 = 2

d) (x + 2)^2 + (y - 3)^2 = 2

Answer 1

The correct equation of the circle with center (2, -3) and radius 2 is (x - 2)^2 + (y + 3)^2 = 4, which matches option a).

Step-by-step explanation:

The equation of a circle in standard form is given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. In this case, the circle is centered at (2, -3) and the radius is 2. Thus, substituting the center coordinates (h = 2 and k = -3) and the radius (r = 2) into the standard form equation, we get the equation (x - 2)^2 + (y + 3)^2 = 2^2, which simplifies to (x - 2)^2 + (y + 3)^2 = 4. Therefore, the correct answer is option a).