Answer:
The equation of the circle is (x + 3)² + (y + 5)² = 36
Explanation:
* Lets revise the standard form of the equation of the circle
- The center-radius form of the circle equation is in the format
(x – h)² + (y – k)² = r², where the center is the point (h, k) and
the radius is r.
- This form of the equation is helpful, because you can easily find
the center and the radius.
* Now lets solve the problem
∵ The center of the circle is (-3 , -5)
∵ The center of the circle in the equation is (h , k)
∴ h = -3
∴ k = -5
∴ The equation of the circle is (x - -3)² + (y - -5)² = r²
∴ The equation is (x + 3)² + (y + 5)² = r²
* Now lets find the value of r²
∵ The length of the radius of the circle is 6 units
∴ r = 6
∴ r² = (6)² = 36
∴ The equation of the circle is (x + 3)² + (y + 5)² = 36