Is the given point interior, exterior, or on the circle (x + 2)2 + (y - 3)2 = 81? p(8, 4)

From the equation we see that the center of the circle is at (-2,3) and the radius is 9.

So using the distance formula we can see if the distance from the center to the point (8,4) is 9 units from the center of the circle...

d^2=(8--2)^2+(4-3)^2  and d^2=r^2=81 so

81=10^2+1^2

81=101  which is not true...

So the point (8,4) is √101≈10.05 units away from the center, which is greater than the radius of the circle.  

Thus the point lies outside or on the exterior of the circle...

The correct graph is the second one, with the points being at (-6,0), (2,0) and reaching down to (-2,-8)