Question

A circle has a diameter with endpoints (-8, 2) and (-2, 6). What is the equation of the circle?

Answer 1

Answer:

Step-by-step 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 :$\frac{-8-2}{2}=-5$

y co-ordinate : $\frac{2+6}{2}=4$

Hence the center is : (-5,4)

Now the distance between these two end points :

$d=\sqrt{(6-2)^2+(-2+8)^2}$

$d=\sqrt{16+36}$

$d=\sqrt{52}$

So radius will be half of this diameter.

$r=\frac{\sqrt{52} }{2}$

Plugging these values in standard equation of circle

$(x-x_{1} )^2+(y-y_{1} )^2=r^2$

$(x+5)^2+(y-4)^2=\frac{52}{4}$

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

Hope it will help :)