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

Question

asked Jul 26, 2022 124k views

1 Answer

Kiwon · Answer 1 · 2022-08-01T08:41:08+0000

Answer:

(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!