Answer:
S(-2, 12) lies on the circle
Step-by-step explanation:
Given : Equation of circle : ![(x + 2)^2 + (y - 3)^2 = 81](https://tex.z-dn.net/?f=%28x%20%2B%202%29%5E2%20%2B%20%28y%20-%203%29%5E2%20%3D%2081)
Point: S(-2, 12)
To Find: Is the given point interior, exterior, or on the circle
Solution :
After substituting the values,
If L.H.S of the given equation is less than R.H.S , So, the given point is interior.
If L.H.S of the given equation is greater than R.H.S , So, the given point is exterior.
If L.H.S =R.H.S , So, the given point is on the circle.
![(-2 + 2)^2 + (12 - 3)^2 = 81](https://tex.z-dn.net/?f=%28-2%20%2B%202%29%5E2%20%2B%20%2812%20-%203%29%5E2%20%3D%2081)
![(0)^2 + (9)^2 = 81](https://tex.z-dn.net/?f=%280%29%5E2%20%2B%20%289%29%5E2%20%3D%2081)
![81 = 81](https://tex.z-dn.net/?f=81%20%3D%2081)
Thus L.H.S =R.H.S
Hence the given point S(-2, 12) lies on the circle ![(x + 2)^2 + (y - 3)^2 = 81](https://tex.z-dn.net/?f=%28x%20%2B%202%29%5E2%20%2B%20%28y%20-%203%29%5E2%20%3D%2081)