Question

When graphed, the circle with equation

x2 + y2 - 14x + 10y + 65 = 0

will lie ENTIRELY in which Quadrant?

Answer 1

we can rewrite your equation as follows:
\[(x-7)^{2}+(y+5)^{2}=9\]
namely, you circle has the centre located at (7,-5) and radius equals to 3, sinc 3<|-5| and 3<7, your circle lie entirely in the fourth quadrant