Question

Is the given point interior, exterior, or on the circle (x + 2)2 + (y - 3)2 = 81?S(-2, 12)

Answer 1

(x + 2)² + (y - 3)² = 81
x=-2, y=12

(-2 + 2)² + (12-3)² = 81
0² + 9² = 81
81 = 81

The given point S(-2, 12) is on the circle

Answer 2

S(-2, 12) lies on the circle

Explanation:

Given : Equation of circle :
`(x + 2)^2 + (y - 3)^2 = 81`

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`

`(0)^2 + (9)^2 = 81`

`81 = 81`

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`