# How do you write an equation for a circle with Point A is (4, -2) Point B is (10,6) as diameters?

##### 1 Answer

We must first find the length of the diameter and the center of the circle.

The center is an equal distance from all points inside a circle. Therefore, we can use the midpoint formula

The center will therefore be at

Now for the length of the diameter.

This can be found by using the distance theorem, a simple variation on pythagorean theorem.

Hence, the diameter measures

Solving for r:

Now that we know our radius, we can substitute what we know into the equation of the circle, of the form mentioned above:

Here is the graph of this relation (note: it's not a function, since every value of x is not only with one value of y)

**Practice exercises:**

- Determine the equation of the circle who's diameter ends at the points
#(-1, -4)# and#(3, -5)# .

Hopefully this helps, and good luck!