Question

(a) Find the center and radius, then (b) graph the circle:$5x^2+5y^2=125$

Short answer

The center and the radius of the circle are $(0,0)$ and $5$respectively. The graph of this circle is:

Step-by-step solution

Part (a) Step 1. Given information.

The equation of the circle is$5x^2+5y^2=125$

We have to find radius and center.

Also, we have to graph this circle.

Part (a) Step 2. Compare with the standard form of a circle to find radius and center 

We have, $5x^2+5y^2=125$

Divide both sides by $5$

$x^2+y^2=25$

Compare it with the standard form,

role="math" localid="1645267211821" ${(x-h)}^2+{(y-k)}^2=r^2$

We have, $(h,k)=(0,0)$

where $(h,k)$is the centre of the circle.

$r=5$

Part (b) Step 1. Graph the circle using radius and center 

The graph is: