Question

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?

Answer 1

r = ✔ 5 units

distance = ✔ 5 units

✔ yes

Answer 2

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