Question

Find the center and radius of each circle. Graph each circle by hand. Determine the intercepts of the graph of circle

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

Short answer

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

$x$axis interception point of $x^2+y^2-2x+4y-4=0$is $\left(1\pm \sqrt{5},0\right)$and y axis is $\left(0,2\left(\sqrt{2}-1\right)\right),\left(0,-2\left(1+\sqrt{2}\right)\right)$

The graph for the equation is .

Step-by-step solution

Step 1. Given information.

Consider the given equation .

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

Step 2. Using the given equation and compare it with the equation of circle. x2+y2+2gx+2fy+c=0

Compare the equation.

$$\begin{gathered} 2g=-2 \\ g=-1 \end{gathered}$$

Further simplify.

$$\begin{gathered} 2f=4 \\ f=2 \end{gathered}$$

$c=-4$

Step 3. Using formula to find radius r=g2+f2-c.

$$\begin{gathered} r=\sqrt{1^2+2^2+4} \\ r=3 \end{gathered}$$

Step 4. Plot the graph.

The graph for the equation is shown below.