Which of the following is the equation of a circle with center (-2,3) and a radius r = 5?
The equation of a circle with center (a,b) and radius r is:
(x-a)^2 + (y-b)^2 = r^2
Substituting a=-2, b=3, and r=5:
(x+2)^2 + (y-3)^2 = 25
The equation of a circle with center (h, k) and a radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center is (-2, 3) and the radius is 5. So, the equation would be:
(x - (-2))^2 + (y - 3)^2 = 5^2
Simplifying this equation, we get:
(x + 2)^2 + (y - 3)^2 = 25
Therefore, the equation of the circle with center (-2,3) and a radius of 5 is (x + 2)^2 + (y - 3)^2 = 25.