Question

find the equation in standard form for the circle with center (0, 7) and radius 9.

Explanation:

Step1: Recall circle - standard form

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

Step2: Identify values of $h$, $k$, and $r$

Given that the center is $(0,7)$, so $h = 0$, $k = 7$, and the radius $r = 9$.

Step3: Substitute values into the formula

Substitute $h = 0$, $k = 7$, and $r = 9$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 0)^2+(y - 7)^2=9^2$.

Step4: Simplify the equation

$(x - 0)^2=x^2$ and $9^2 = 81$, so the equation is $x^2+(y - 7)^2=81$.

Answer:

$x^2+(y - 7)^2=81$