Question

Select interior, exterior, or on the circle (x - 5)2 + (y + 3)2 = 25 for the following point.

(5,-3)

Answer 1

Explanation:

One of the ways that you can get the answer without much thought is to graph it as I have done below.

What you should see is that the point (5,-3) is the center of the circle you just plotted. That being the case and since the center of a circle is always in the interior of the circle, the answer is Interior.

One other way is to put x=5 and y = -3 into the original equation.

(5 - 5)^2 + (-3 + 3)^2

0 + 0 = ? well it equals zero. The center will always do that.

If you still remain unconvinced, what would happen if you were asked to plot (11,-3)

(11 - 5)^2 + (-3 - -3)^2 = ? 6^2 + 0 = 36

36 is larger than 25 so the point 11,-3 is outside the circle.