Question

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

Answer 1

Answer:

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

Step-by-step 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!