Q 12. - Precalculus Enhanced with Graphing Utilities

Question

Find the center and radius of the circle

$x^2+y^2+4x-2y-4=0$. Graph this circle.

Step-by-Step Solution

Answer

Center and radius are $\left(-2,1\right)$ and $3$.

Graph of the equation shown below.

Step 1. Given information.

Consider the given equation of the circle .

$x^2+y^2+4x-2y-4=0$

Step 2. Using the standard form of circle to rewrite the given equation in standard form. x - h 2 + y - k 2 = r 2 where h , k are the center and r is radius.

$$\begin{gathered} x^2+4x-2y-4+y^2=0 \\ {\left(x-\left(-2\right)\right)}^2+{\left(y-1\right)}^2=3^2 \end{gathered}$$

Therefore the circle properties . $\left(h,k\right)=\left(-2,1\right)$ and $r=3$

Ste[p 3. Plot the graph.

The graph of the given equation is shown below.