Question

The diameter of a circle has endpoints at `(-2, 3)` and `(6, 3)`. What is an equation of the circle?

Answer 1

First, use the mid point formula to find the center of the circle.

Midpoint formula: `((x_1 + x_2)/2, (y_1 + y_2)/2)`

`= (4/2, 6/2)`

`= (2, 3)`

Since the points are located on a straight line, our next task, finding the radius, is a whole lot easier.

`r = 2 - (-2)`

`r = 4`

The radius is 4.

Now, using the formula `(x - h)^2 + (y - k)^2 = r^2`, where r is radius and (h, k) is the center, we will finally be able to find the equation of the circle:

`(x - 2)^2 + (y - 3)^2 = 16`

Here is the graph of your circle:

graph{(x - 2)^2 + (y - 3)^2 = 16 [-10, 10, -5, 5]}

Hopefully this helps!