Question

HELP DUE IN 15 MINS!

Answer 1

Answer:

r = $2\sqrt{5}$

$(x - 3)^{2} + ( y - 2)^{2} = 20$

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Step-by-step explanation:

the radius is the distance between (3, 2) and (5, -2)

$r^{2}$ = ${(3 - 5)^{2} + (2 + 2)^{2} }$

    =  $(-2)^{2} + 4^{2}$

    =  4 + 16 = 20

r = $\sqrt{20 } = 2\sqrt{5}$

Equation of circle:   $(x - 3)^{2} + ( y - 2)^{2} = 20$

Answer 2

Answer:

Radius: $2\sqrt{5}$

Equation of circle: $(x-3)^2+(y-2)^2=20$

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:

$r=\sqrt{(5-3)^2+(2-(-2))^2},\\r=\sqrt{2^2+4^2},\\r=\sqrt{20}=\boxed{2\sqrt{5}}$

The equation of a circle with radius $r$ and center $(h, k)$ is given by:

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

What we know:

• radius of $2\sqrt{5}$
• center at $(3, 2)$

Substituting known values, we get:

$(x-3)^2+(y-3)^2=(2\sqrt{5})^2,\\\boxed{(x-3)^2+(y-2)^2=20}$