Question

find the equation of the circle for which endpoints of the diameter are (-6, -3) and (4, 7)

Answer 1

Find the midpoint use the coordinate with the distance-like formula to find the equation of the circle

Answer 2

Use distance formula to get the length of the diameter:
\[\sqrt{(x-x_1)^2 + (y-y_1)^2} = d\]
\[d = 2r\]
Find \(r\)

Then use the two points to get the midpoint using midpoint formula:\[(x_{mid},y_{mid}) = (\frac{(x+x_1)}{2},\frac{(y+y_1)}{2})\]

Thus, you now have your radius, and the midpoint co-ordinates.

Use that in the circle equation: \[(x-x_{mid})^2 + (y-y_{mid})^2 = r^2\]

Getting this? :)