Answer:
(x - 4)² + (y + 9)² = 25
Explanation:
The equation of a circle is written as seen below.
(x – h)² + (y – k)² = r²
Where (h,k) represents the center of the circle and r represents the radius
We want to find the equation of a circle that has a center at (4,-9) and a radius of 5.
We know that (h,k) represents the center so h = 4 and k = -9
We also know that r represents the radius so r = 5
Now to find the equation of this specific circle we simply plug in these values into the equation of a circle formula
Equation: (x – h)² + (y – k)² = r²
h = 4, k = -9 and r = 5
Plug in values
(x - 4)² + (y - (-9))² = 5²
5² = 25
The two negative signs in front of the 9 cancel out and it changes to + 9
The equation of a circle with a center at (4,-9) and a radius of 5 is
(x - 4)² + (y + 9)² = 25