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