Answer:
r = [tex]2\sqrt{5}[/tex]
[tex](x - 3)^{2} + ( y - 2)^{2} = 20[/tex]
Is this a live test question or a homework question?
Step-by-step explanation:
the radius is the distance between (3, 2) and (5, -2)
[tex]r^{2}[/tex] = [tex]{(3 - 5)^{2} + (2 + 2)^{2} }[/tex]
= [tex](-2)^{2} + 4^{2}[/tex]
= 4 + 16 = 20
r = [tex]\sqrt{20 } = 2\sqrt{5}[/tex]
Equation of circle: [tex](x - 3)^{2} + ( y - 2)^{2} = 20[/tex]
Answer:
Radius: [tex]2\sqrt{5}[/tex]
Equation of circle: [tex](x-3)^2+(y-2)^2=20[/tex]
Step-by-step explanation:
The radius of a circle is equal to the distance between the center of the circle and any point on the circle. Therefore, we have:
[tex]r=\sqrt{(5-3)^2+(2-(-2))^2},\\r=\sqrt{2^2+4^2},\\r=\sqrt{20}=\boxed{2\sqrt{5}}[/tex]
The equation of a circle with radius [tex]r[/tex] and center [tex](h, k)[/tex] is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex].
What we know:
Substituting known values, we get:
[tex](x-3)^2+(y-3)^2=(2\sqrt{5})^2,\\\boxed{(x-3)^2+(y-2)^2=20}[/tex]
