Question1. What is the equation, center, and radius of the circle? $$\begin{array}{l} x^{2}+2 x+y^{2}+6 y-7=0 \\ x^{2}+2 x+y^{2}+6 y=7 \\ x^{2}+2 x+17 y^{2}+6 y=7+1 \\ (x+1)^{2}+y^{2}+6 y=8 \\ (x+1)^{2}+y^{2}+6 y+9<8+9 \\ (x+1)^{2}+(y+3)^{2}=17 \end{array}$$

Studdy Solution
Identify the center and radius from the standard form:
The standard form of a circle is:
$$(x - h)^2 + (y - k)^2 = r^2$$
From the equation:
$$(x + 1)^2 + (y + 3)^2 = 17$$
The center $(h, k)$ is $(-1, -3)$ and the radius $r$ is $\sqrt{17}$.
The equation of the circle is:
$$(x + 1)^2 + (y + 3)^2 = 17$$
The center of the circle is:
$$(-1, -3)$$
The radius of the circle is:
$$\sqrt{17}$$