Answer:
The center of the circle is (-3 , 5) and the length of the radius is 9 units
Step-by-step 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 equation is (x + 3)² + (y - 5)² = 81
- By comparing the two equations
∵ (x – h)² + (y – k)² = r² and (x + 3)² + (y - 5)² = 81
# x - h = x + 3
∴ -h = 3 ⇒ divide both sides by -1
∴ h = -3
# y - k = y - 5
∴ k = 5
# h and k are the coordinates of the center of the circle
∴ The center of the circle is (-3 , 5)
# r² = 81 ⇒ take √ for both sides
∴ r = 9
∴ The length of the radius = 9 units
* The center of the circle is (-3 , 5) and the length of the radius is 9 units
