Question

ⓐ Find the center and radius, then ⓑ graph the circle:${(x-3)}^2+{(y-1)}^2=16$

Short answer

The center and the radius of the circle are $(3,1)$and $4$respectively. The graph of this circle is:

Step-by-step solution

Step 1. Given information.

The equation of the circle is ${(x-3)}^2+{(y-1)}^2=16$.

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

Write the given equation ${(x-3)}^2+{(y-1)}^2=16$in standard form ${(x-h)}^2+{(y-k)}^2=r^2$.

${(x-3)}^2+{(y-1)}^2=4^2$

Center$=(3,1)$

Radius$=4$

Part (b) Step 3. Graph the circle using radius and center

The circle is graphed as: