Answer :
Given
The center of the circle is (7,-2).
And, it passes through (-10,0).
To find the equation of the circle.
Explanation:
It is given that,
The center of the circle is (7,-2).
And, it passes through (-10,0).
Then, the standard form of the circle is given by,
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \Rightarrow(x-7)^2+(y+2)^2=r^2\text{ \_\_\_\_\_\_\lparen1\rparen} \end{gathered}[/tex]Since it passes through (-10,0).
Then,
[tex]\begin{gathered} (-10-7)^2+(0+2)^2=r^2 \\ 289+4=r^2 \\ r^2=293 \end{gathered}[/tex]Hence, the equation of the circle is,
[tex](x-7)^2+(y+2)^2=293[/tex]