Question

A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is

units. The point (-7,
) lies on this circle.

Answer 1

5, -1

Explanation:

Answer 2

The radius, r, of the circle is the distance from the center to any point on the circle.

r = √[(1-(-3))2+(5-2)2] = √25 = 5

An equation of the circle with center (h,k) and radius r is:

(x-h)2 + (y-k)2 = r2

So, in this problem, we have (x+3)2+(y-2)2=25.

To find a point on the circle with x-coordinate -7, replace x by -7 in the equation of the circle and solve for y:

(-7+3)2+(y-2)2 = 25

16 + (y-2)2=25

(y-2)2 = 9

y-2 = 3 or -3

So, y = 5 or -1

The points (-7,5) and (-7,-1) both lie on the circle.