Answer:
[tex](x+4)^2+(y-8)^2=85[/tex]
Step-by-step explanation:
The standard equation for a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the center and r is the radius.
We know that the center is (-4, 8). So, substitute -4 for h and 8 for k:
[tex](x-(-4))^2+(y-8)^2=r^2\\[/tex]
Simplify:
[tex](x+4)^2+(y-8)^2=r^2[/tex]
Now, we will need to find r.
We know that it passes through the point (-2, -1). So, we can substitute -2 for x and -1 for y and solve for r. So:
[tex](-2+4)^2+(-1-8)^2=r^2[/tex]
Evaluate:
[tex](2)^2+(-9)^2=r^2[/tex]
Square:
[tex]4+81=r^2[/tex]
Add:
[tex]r^2=85[/tex]
So, r squared is 85.
We don’t actually have to solve for r itself, since we will have to square it anyways.
So, we have:
[tex](x+4)^2+(y-8)^2=r^2[/tex]
Substituting 85 for r squared, we get:
[tex](x+4)^2+(y-8)^2=85[/tex]
And we have our equation.
