How do you write an equation for a circle with diameter are P(−2, 2) and Q(6, −6)?
I guess you meant end points of the diameter are
First, you take out the midpoint of the line joining points
Let it be
( Using midpoint formula)
Since, the midpoint of a diameter is the centre of the circle, and standard coordinate of the centre is
Then, take out the length of the diameter using distance formula,
Now, we have
Let us substitute these in the standard equation of a circle,
This is our required equation.
Hope this helps :)
Pretty long one, though.