Question

The coordinates below are the endpoints of the diameter.

Find the coordinates of the center


Find the length of the radius.



Write the equation of the circle standard form.

Answer 1

`(x+1)^(2) +(y+0.5)^(2) =5.3^(2)`

Explanation:

The endpoints of the diameter are (-5,3) and (3,-4).

We know that the mid point of the diameter is the center of the circle, and half of its length is the radius. Let's find the center first.

`C=((-5+3)/(2) ,(3-4)/(2) )\\C=((-2)/(2) ,(-1)/(2) )\\C=(-1, -0.5)`

The length of the diameter can be found with the formula below

`d=\sqrt{(y_(2) -y_(1) )^(2)+(x_(2) -x_(1) )^(2) } \\d=\sqrt{(-4-3)^(2) +(3-(-5))^(2) } =√(49+64)\\ d=√(113) \approx 10.6`

Therefore, the diameter is 10.6 units, approximately.

So, the radius is

`r=(d)/(2) \approx (10.6)/(2)=5.3`

Therefore, the radius is 5.3 units.

Now we can find the equation of the circle

`(x+1)^(2) +(y+0.5)^(2) =5.3^(2)`