[tex]\boxed{\left(x-7\right)^{2}+\left(y+8\right)^{2}=41}[/tex]
Explanation:
The center-radius form of the circle equation is given by the form:
[tex](x-h)^2+(y-k)^2=r^2 \\ \\ \\ Where: \\ \\ (h,k):Center \\ \\ r:Radius[/tex]
So, we know that:
[tex](h,k)=(7,-8)[/tex]
So we just need to find the radius. We know that the distance from the center of the circle to any point equals the radius of the circle. Hence, by using distance formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} \\ \\ (x_{1},y_{1})=(7,-8) \\ \\ (x_{2},y_{2})=(2,-4) \\ \\ \\ r=\sqrt{(2-7)^2+(-4-(-8))^2}=\sqrt{41}[/tex]
Finally, the equation of the circle is:
[tex]\boxed{\left(x-7\right)^{2}+\left(y+8\right)^{2}=41}[/tex]
And the graph is shown below.
Learn more:
Parametrization of circle: https://brainly.com/question/10178625
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