Question

HELP THIS IS DUE TODAY I WILL NAME YOU THE BRAILIEST!!!!!!!

Determine the equation of the circle graphed below.

Answer 1

`(x-4)^2+(y+3)^2=20`

Explanation:

The equation of a circle with center
`(h,k)` and radius
`r` is given by
`(x-h)^2+(y-k)^2=r^2`.

What we know:

• Center at
  `(4,-3)`

To find the radius, we can use the distance formula. For points
`(x_1, y_1)` and
`(x_2,y_2)`, the distance between them is
`√((x_2-x_1)^2+(y_2-y_1)^2)`.

Let

`(x_1,y_1)\implies (-4, -3),\\(x_2,y_2)\implies (8,-1)`

`r=√((8-4)^2+(-1-(-3))^2),\\r=√(4^2+2^2),\\r=√(20)=2√(5)`

Thus, the equation of this circle is

`(x-4)^2+(y-(-3))^2=√(20)^2,\\\boxed{(x-4)^2+(y+3)^2=20}`