The point (0, 5) lies on a circle that is centered at the origin. does (–3, –4) also lie on the circle? identify the radius from the graph. r = units determine the distance from the center to (–3, –4) using the distance formula. distance = units compare the radius to the distance. does the point (–3, –4) also lie on the circle?

We know that

the equation of a circle is
(x-h)²+(y-k)²=r²
where the center is the point (h,k)
r is the radius 
if the center is the origin
so
(h,k) is (0,0)

the radius is the distance from point (0,5) to the origin (0,0)
r=√[(-5)²+(0)²]> r=√25> r=5 units

the equation is
(x-h)²+(y-k)²=r²> (x-0)²+(y-0)²=5²> (x)²+(y)²=25

Does the point (–3, –4) also lie on the circle?
the distance from the center to (–3, –4) is
d=√[(-4)²+(-3)²]> d=√25>d=5 units

d=r
therefore
the point (-3,-4) also lie on the circle