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)?

(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

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: