Q 31. - 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 .

$3x^2+3y^2-6x+12y=0$

Step-by-Step Solution

Answer

Center and the radius of given circle are $\left(-1,2\right)$ and $\sqrt{5}$ and the intercepts of x axis are $\left(2,0\right) ,\left(0,0\right)$ and $y$ axis are $\left(0,0\right) ,\left(0,-4\right)$.

Step 1. Given information.

Consider the given equation of circle .

$3x^2+3y^2-6x+12y=0$

Step 2. Using the equation of circle. x 2 + y 2 + 2 g x + 2 f y + c = 0

Compare the given equation with the equation of circle to find center and radius.

$$\begin{gathered} 2g=-2 \\ g=-1 \\ 2f=4 \\ f=2 \\ c=0 \end{gathered}$$

Further simplify.

$r=\sqrt{g^2+f^2-c}$

Substitute the value of $h,k,r$ to find radius.

$$\begin{gathered} r=\sqrt{{\left(-1\right)}^2+2^2-0} \\ r=\sqrt{5} \end{gathered}$$