A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is how many units. The point (-7,? ) lies on this circle.

we know that

the equation of a circle is
(x-h)²+(y-k)²=r²
(h,k) is the center----------> (-3,2)

the radius is the distance point (-3,2) and point (1, 5)
d=√(5-2)²+(1+3)²-------> d=√9+16----------> d=5

radius=5 units

equation is
(x+3)²+(y-2)²=25

for x=-7
(-7+3)²+(y-2)²=25-------> 16+y²-4y+4=25
y²-4y-5=0

using a graph tool -------> to resolve the second order equation

see the attached figure

the solution is 
y1=-1
y2=5

the point will be
(-7,-1)
(-7,5)