Question

What is the equation of the circle with endpoints of the diameter of a circle are (1,-1) and (9,5)?

Answer 1

`(x-5)^2+(y-2)^2=25`

Explanation:

A general circle centred at `(a,b)` and having radius `r` has equation `(x-a)^2+(y-b)^2=r^2`.

The centre of the circle would be the midpoint between the 2 diameter endpoints, ie `((1+9)/2,(-1+5)/2)=(5,2)`

The radius of the circle would be half the diameter, ie. half the distance between the 2 points given, that is

`r=1/2(sqrt((9-1)^2+(5+1)^2))=5`

Thus the equation of the circle is

`(x-5)^2+(y-2)^2=25`.