Q. 30 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

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 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. x 2 + y 2 + 2 g x + 2 f y + 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 = g 2 + f 2 - 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.