Question

Find (a) the center (h, k) and radius r of each circle; (b) graph each circle; (c) find the intercepts if any of the equation$2x^2+8x+2y^2=0$

Short answer

a) center (h ,k), and the radius of the given equation are (-2,0) and 2

b) graph of the given equation is given below

Step-by-step solution

Part (a) step 1. Given information  

Given the equation of the circle is $2x^2+8x+2y^2=0$

We have to Find (a) the center (h, k) and radius r of circle

 Part (a) Step 2. Rewriting the equation of a circle   

Here equation is in the form$$\begin{gathered} 2x^2+8x+2y^2=0 \\ {x}^2+4x+y^2=0dividingby2getequationins\tan dardform \\ (x^2+4x)+y^2=0 \end{gathered}$$

Part (a) step 3.  Find center and radius  

complete the square of each expression in parentheses, we get an

$$\begin{gathered} (x^2+4x)+y^2=0 \\ (x^2+4x+4)+y^2=4,\sin ceanynumberaddedontheleftsidemustaddtorightside \\ {(x+2)}^2+{(y-0)}^2=2^{2}sothiss\tan dardformofthecircleequaionwithcenterandradius \\ hencecenteris(-2,0)andradiusis2. \end{gathered}$$

Here x intercept and y intercept are both at 0.

Part (b)  step 1. Given information

Here given equation of a circle is$2x^2+8x+2y^2=0$

We need to sketch the graph

 Part (b) step 2. Graph of the equation of the circle  

the graph of the given equation with center(-2,0) and radius 2 is given below