Question

Write the equation of a circle with endpoints of the diameter at (4, -3) and (-2, 5).
Show your work for credit.

Answer 1

ok you need two things, first the center, then the radius
do you know how to find them?

Answer 2

center is the midpoint of the line segment with endpoints \((4, -3)\) and \( (-2, 5)\)
you find it by taking the average in each coordinate
\((\frac{4-2}{2},\frac{5-3}{2})\) or \((1,1)\)

Answer 3

the radius you get by the distance formula.
you really only need the square of the radius, not the radius, so you can dispense with the annoying radical.
the square of the distance between \((1,1)\) and \(( 4,-3)\) is
\[(4-1)^2+(-3-1)^2=3^2+4^2=25\]

Answer 4

now use
\[(x-h)^2+(y-k)^2=r^2\] with
\[h=1,, k=1, r^2=25\]