Question

write the standard form equation for circle j with a center at the origin and a diameter of 18.

Explanation:

Step1: Find the radius

The radius $r$ of a circle is half of the diameter $d$. Given $d = 18$, then $r=\frac{d}{2}=\frac{18}{2}=9$.

Step2: Recall the standard - form equation of a circle

The standard - form equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^2+(y - k)^2=r^2$. Since the center is at the origin $(0,0)$, $h = 0$ and $k = 0$.

Step3: Substitute the values into the equation

Substitute $h = 0$, $k = 0$, and $r = 9$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x - 0)^2+(y - 0)^2=9^2$, which simplifies to $x^{2}+y^{2}=81$.

Answer:

$x^{2}+y^{2}=81$