Question

What is the standard form of the equation of a circle that has its center at (-2, -3) and passes through the point (-2, 0)?

Answer 1

Answer:

(x - h)^2 + (y - k)^2 = 3^2

Step-by-step explanation:

The most general standard form here is

(x - h)^2 + (y - k)^2 = r^2.  Since we know the center is at (-2, -3), we rewrite this equation as

(x + 2)^2 + (y + 3)^2 = r^2.

Note that the center (-2, -3) and the point (-2, 0) lie on the same vertical line, and that the vertical distance from the center to this point is 3.  This is also the radius of the circle.  Thus, the equation of this circle is:

(x - h)^2 + (y - k)^2 = 3^2