Question

find the center and radius of the circle.
x² + y² - 4x - 18y - 7 = 0
the center is (2,9).
(type an ordered pair.)
the radius is
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Rewrite the equation by completing the square for x and y terms.

The general equation of a circle is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center and $r$ is the radius.
For the given equation $x^{2}+y^{2}-4x - 18y-7 = 0$, we complete the square:
\[

$$\begin{align*} x^{2}-4x+y^{2}-18y&=7\\ x^{2}-4x + 4+y^{2}-18y+81&=7 + 4+81 \end{align*}$$

\]

Step2: Factor the left - hand side and simplify the right - hand side.

We get $(x - 2)^{2}+(y - 9)^{2}=92$.

Answer:

$2\sqrt{23}$