Question

find equation of a circle Center lies on the x-axis
tangent to x=7 and x=-13

Answer 1

hint:
we have to consider the subsequent two algebraic systems:
\[\begin{gathered}
\left\{ \begin{gathered}
{x^2} + {y^2} + ax + b = 0 \hfill \\
x = 7 \hfill \\
\end{gathered} \right. \hfill \\
\left\{ \begin{gathered}
{x^2} + {y^2} + ax + b = 0 \hfill \\
x = - 13 \hfill \\
\end{gathered} \right. \hfill \\
\end{gathered} \]
afeter a substitution of the second equation into the first one, we get two quadratic equations.
We have to set to zero the discriminats of each equation respectively, so we find the values of the parameters a and b

Answer 2

another way to do this is to translate the center (0,0) to the midpoint (-3,0)
the radius is 10.
you can use the equation
$$
\Large (x-h)^2 + (y-k)^2 = r^2
$$