Question

Find the equation for the circle with center (-1, - 4) and passing through (-5,5).

Answer 1

`(x+1)^2+(y+4)^2=97`

Explanation:

Hi there!

Equation of a circle centered at (h,k):

`(x-h)^2+(y-k)^2=r^2` where r is the radius

1) Plug in the center

`(x-(-1))^2+(y-(-4))^2=r^2\\(x+1)^2+(y+4)^2=r^2`

2) Plug in the given point and solve for r²

`(x+1)^2+(y+4)^2=r^2`

Plug in (-5,5)

`(-5+1)^2+(5+4)^2=r^2\\(-4)^2+(9)^2=r^2\\16+81=r^2\\r^2=97`

3) Plug r² back into the equation

`(x+1)^2+(y+4)^2=r^2\\(x+1)^2+(y+4)^2=97`

I hope this helps!