Question

Type the correct answer in each box. A circle is centered at the point (5, -4) and passes through the point (-3, 2).

The equation of this circle is (x + )2 + (y + )2 =

Answer 1

Hello,

C=(5,-4)
P=(-3,2)
|CP|²=(-3-5)²+(2+4)²=64+36=100

(x-5)²+(y+4)=100

Answer 2

Remember the  equation of the circle:

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

where $(h,k)$ is the center of the circle and $r$ is its radio.

You already have the center, that is $(h,k)=(5,-4)$ and hence we have

$h=5$ and $k=-4$ (be careful with the signs).

For the radio we use the formula of distance between two points:

$r^2 = (-3-5)^2 + (2-(-4))^2= 64 + 36 = 100 = 10 ^2$

So the radio is 10.

Finally we replace tha data in the equation of the circle to obtain:

$(x-5)^2 + (y-(-4))^2=10^2\\\\(x-5)^2 + (y+4)^2=10^2$