Question

Write the equation of this circle in standard form. Please be quick.

Answer 1

Standard Equation of a Circle

Given a circle of radius r and centered at (h,k), the standard equation of the circle is given as:

`(x-h)^2+(y-k)^2=r^2`

We are given the graph of a circle and from the data, we can get there we will find the center and the radius.

The center is clearly visible at (2,6)

The radius is half the length of the diameter. It can be clearly visualized from point (2,3) to the point (2,9).

The diameter is d = 9-3 = 6, thus the radius is r = 6/2 = 3

Now we plug all the numbers into the formula:

`(x-2)^2+(y-6)^2=3^2`

Operating:

`(x-2)^2+(y-6)^2=9`

This is the required equation of the circle