Answer:
(x-5)^2+(y+4)^2=100
Step-by-step explanation:
As we know the given points
Center = (5, -4)
and
Point on circle = (-3,2)
The distance between point on circle and center will give us the radius of circle
So,
The formula for distance is:
[tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}\\Taking\ center\ as\ point\ 1\ and\ the\ other\ point\ as\ point\ 2\\d=\sqrt{(-3-5)^{2}+(2-(-4))^{2}}\\d=\sqrt{(-8)^{2}+(2+4)^{2}}\\d=\sqrt{(-8)^{2}+(6)^{2}}\\\\d=\sqrt{64+36}\\d=\sqrt{100} \\ d=10\\So\ the\ radius\ is\ 10[/tex]
The standard form of equation of circle is:
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where h and k are the coordinates of the center. So putting in the value:
[tex](x-5)^{2}+(y-(-4))^{2}=(10)^{2}\\(x-5)^{2}+(y+4)^{2}=100[/tex]
