Question

In the following exercises, write the standard form of the equation of the circle with the given radius and center $(0,0)$.

Radius is $7$.

Short answer

The standard form of the equation of the circle is$x^2+y^2=49$.

Step-by-step solution

Step 1. Given and explanation.

We have the center of the circle as $(0,0)$and the radius is $7$.

We know that the standard form of the equation of circle is ${(x-h)}^2+{(y-k)}^2=r^2$, where $(h,k)$is the coordinate of center of circle and $r$is radius.

Applying this and simplifying the expression will give us the equation.

Step 2. Finding equation of circle.

We have the center, i.e., $(h,k)$as $(0,0)$and radius, i.e., $r$as $7$.

Substituting these values in the standard form of equation gives us,
${(x-0)}^2+{(y-0)}^2={\left(7\right)}^2$
Simplifying this gives the equation of circle as $x^2+y^2=49$.