Question

A circle whose center is at (5, -3) and which passes through the point (7, -8) has a radius equal to

Answer 1

The distance from the center to any point on the circle is the radius.
Use the distance formula to find the radius:
d = $\sqrt{(x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }$
   = $\sqrt{(5 - 7)^{2} + (-3 + 8})^{2}}$
   = $\sqrt{(-2)^{2} + (5})^{2}}$
   = $\sqrt{(4 + 25)}$
   = $\sqrt{29}$

Answer: the radius of the circle is $\sqrt{29}$