Question

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

Q(3, 0)

Answer 1

Answer: interior

From the given equation you know that the center of the circle is (-2,3) and the radius is √81 = 9

You know that all the points that are at a distance smaller than 9 from the center (-2,3) are interior. This results pretty obvious to me but I will make the calculations for you.

Use the distance formula for the points (3,0) and (-2,3):

d = √[ (x1 -x2)^2 + (y1 -y2)^2 ] = √[ (3-(-2))^2 + (0 - 3)^2 ] =√[25 + 9] = √36 = 6

Given that 6 < 9, the point is interior to the circle.