Answer:
The equation of the circle is
[tex](x-5)^{2} +(y+4)^{2}=100[/tex]
Step-by-step explanation:
we know that
The equation of the circle in center radius form is equal to
[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]
In this problem we have
[tex](h,k)=(5,-4)[/tex]
so
[tex](x-5)^{2} +(y+4)^{2}=r^{2}[/tex]
To find the radius substitute the value of x and the value of y of the point [tex](-3,2)[/tex] in the equation
[tex](-3-5)^{2} +(2+4)^{2}=r^{2}[/tex]
[tex](-8)^{2} +(6)^{2}=r^{2}[/tex]
[tex]100=r^{2}[/tex]
[tex]r=10\ units[/tex]
substitute
[tex](x-5)^{2} +(y+4)^{2}=10^{2}[/tex]
[tex](x-5)^{2} +(y+4)^{2}=100[/tex]
see the attached figure to better understand the problem
