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 :[tex]\frac{-8-2}{2}=-5[/tex]
y co-ordinate : [tex]\frac{2+6}{2}=4[/tex]
Hence the center is : (-5,4)
Now the distance between these two end points :
[tex]d=\sqrt{(6-2)^2+(-2+8)^2}[/tex]
[tex]d=\sqrt{16+36}[/tex]
[tex]d=\sqrt{52}[/tex]
So radius will be half of this diameter.
[tex]r=\frac{\sqrt{52} }{2}[/tex]
Plugging these values in standard equation of circle
[tex](x-x_{1} )^2+(y-y_{1} )^2=r^2[/tex]
[tex](x+5)^2+(y-4)^2=\frac{52}{4}[/tex]
[tex](x+5)^2+(y-4)^2=13[/tex] .................................. This is the answer
Hope it will help :)
