1. A circle with center (-5, 2) is tangent to the y-axis. What is the radius of the circle? What is the equation of the circle?
2. (x - 4)² + (y + 3)² = 36. what is the center and the radius of this circles.
3. Two points in the plane, A(15, 4) and B(15, -8), represent the endpoint of the diameter of a circle. what is the center, radius and equation of this circle.

Step-by-step explanation:

1)  The center lies on the vertical line x = -5 and the the circle is tangent to (touches in one place only) the y-axis.  Thus, the radius is 5.

2)  Starting with (x - h)^2 + (y - k)^2 = r^2 and comparing this to the given

                     (x - 4)^2 + (y + 3)^2 = 6^2

we see that h = 4, k = -3 and r = 6.  The center is at (4, -3) and the radius is 6.

3)  Notice that A and B have the same x-coordinate, x = 15.  The center of the circle is thus (15, -2), where that -2 is the halfway point between the two given points in the vertical direction.   Arbitrarily choose A(15, 4) as one point on the circle.  Then the equation of this circle is

(x - 4)^2 + (y + 3)^2 = r^2 = 6^2, where the 6 is one half of the vertical distance between A(15, 4) and B(15, -8) (which is 12).

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: