Answer:
(x+10)² + (y+5)² = 125
Explanation:
Pre-Solving
We are given that a circle has a center (-10,-5), and passes through the point (-5,5).
We want to write the equation of this circle in the standard equation. The standard equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.
Solving
As we are already given the center point, we can substitute its values into the equation.
Reminder: the equation uses negative values, and we have negative numbers.
(x--10)² + (y--5)² = r²
This can be simplified to:
(x+10)² + (y+5)² = r²
Now, we need to find r².
As the point passes through (-5,5), we can use its values to solve for r².
Substitute -5 as x and 5 as y.
(-5+10)² + (5+5)² = r²
(5)² + (10)² = r²
25 + 100 = r²
125=r²
The radius is 125
Substitute 125 as r².
(x+10)² + (y+5)² = 125