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

The radius of the circle is 5 units

(-7,-1) and (-7,5) lies on the circle

Explanation:

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

Center of the circle is given as (-3,2)

Use center radius form of the circle equation

(x-h)^2 + (y-k)^2 = r^2

(h,k) is the center and r is the radius

h= -3 and k = 2, point (x,y) is (1,5)

`(1+3)^2+(5-2)^2= r^2`

16+9 = r^2

25= r^2 so radius r= 5

The radius of the circle is 5 units

equation of circle is (x+3)^2 + (y-2)^2 = 25

To find out the point we plug in -7 for x

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

16 + (y-2)^2 = 25

Subract 16 from both sides

+ (y-2)^2 = 9

take square root on both sides

y-2=+-3

y= +3+2= 5

y= -3+2= -1

So (-7,-1) and (-7,5) lies on the circle