Question

A circle has a diameter with endpoints (-8, 2) and (-2, 6).

What is the equation of the circle?

Answer 1

Explanation:

Alright, lets get started.

We have given two points that are end point of diameter.

So, the center point will be :

x co-ordinate :
`(-8-2)/(2)=-5`

y co-ordinate :
`(2+6)/(2)=4`

Hence the center is : (-5,4)

Now the distance between these two end points :

`d=√((6-2)^2+(-2+8)^2)`

`d=√(16+36)`

`d=√(52)`

So radius will be half of this diameter.

`r=(√(52) )/(2)`

Plugging these values in standard equation of circle

`(x-x_(1) )^2+(y-y_(1) )^2=r^2`

`(x+5)^2+(y-4)^2=(52)/(4)`

`(x+5)^2+(y-4)^2=13` .................................. This is the answer

Hope it will help :)