Answer:
[tex](x-5)^{2}+(y+4)^{2}=100[/tex]
Explanation:
We have been given the center of the circle as (5, -4) and a point on the circumference as (-3, 2). We first determine the radius of the circle. The radius is the distance from the center to any point on the circumference. Using the distance formula, we have;
[tex]radius=\sqrt{(5--3)^{2}+(-4-2)^{2}}\\radius=\sqrt{64+36}=10[/tex]
The radius of the circle is thus 10 units.
The equation of a circle with center (a,b) and radius r units is given as;
[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]
Plugging in the values given we have;
[tex](x-5)^{2}+(y+4)^{2}=100[/tex]
