Answer
Standard Form: $(x + 5)^2 + (y + 2)^2 = 49$
General Form: $x^2 + y^2 + 10x + 4y - 20 = 0$
Refer to the graph below..
Work Step by Step
The standard form of a circle's equation is $(x−h)^2+(y−k)^2=r^2$ where $r$=radius and $(h,k)$ is the center.
Substitute $r=7, h=-5, \text{ and } k=-2$ in the standard form above to obtain:
$$[x−(-5)]^2+[y-(-2)]^2=7^2\\
(x+5)^2+(y+2)^2=49$$
The general form of the equation of a circle is $x^2+y^2+ax+by+c=0$..
Subtract $49$ from each side of the equation above to obtain:
\begin{align*}
(x+5)^2+(y+2)^2−49=0\\
x^2+10x+25+y^2+4y+4−49=0\\
x^2+y^2+10x+4y−20=0
\end{align*}
With $r=7$ and center at $(-5,-2)$, plot the points $7$ units directly above, below, to the left, and to the right of the circle$. Then, connect these four points using a smooth curve to form a circle.
Refer to the graph above.
