Final answer:
The radius of the circle is 17 units. The y-coordinate of the point (-15, y) that lies on the circle can be either 14 or -16.
Step-by-step explanation:
To find the radius of the circle, we can use the distance formula. The distance between the center of the circle, (-7, -1), and the point on the circle, (8, 7), is the radius. Using the distance formula, we have:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((8 - (-7))^2 + (7 - (-1))^2)
Distance = √((15)^2 + (8)^2)
Distance = √(225 + 64)
Distance = √289
Distance = 17
So, the radius of the circle is 17 units. Now, to find the y-coordinate of the point (-15, y) that lies on the circle, we can substitute x = -15 into the equation of a circle and solve for y:
(x - h)^2 + (y - k)^2 = r^2
(-15 - (-7))^2 + (y - (-1))^2 = 17^2
(-15 + 7)^2 + (y + 1)^2 = 289
(-8)^2 + (y + 1)^2 = 289
64 + (y + 1)^2 = 289
(y + 1)^2 = 289 - 64
(y + 1)^2 = 225
y + 1 = ±√225
y + 1 = ±15
y = -1 + 15 or y = -1 - 15
y = 14 or y = -16
So, the point (-15, 14) or (-15, -16) lies on the circle.