Question

Name the diameter, radius, center, and the equation of the circle with a diameter that has endpoints at (-3, 4) and (5, -2).

Answer 1

If the endpoints of the diameter are known, you can find the center of the circle by finding their midpoint. The midpoint of two points \((x_1,y_1),(x_2,y_2)\) on a line is:
\[(\frac{1}{2}(x_1+x_2) ,\frac{1}{2}(y_1+y_2) )\]
The length of the diameter can be found with the formula for the distance between two points \((x_1, y_1), (x_2, y_2)\):
\[d=\sqrt{(x_1-x_2)^2 + (y_1+y_2)^2}\]
The general formula for a circle with center at \((h,k)\) and radius \(r\) is:
\[(x-h)^2 + (y-k)^2 = r^2\]
You're on your own for the formula for the radius given the diameter :-)

Answer 2

Sorry, that should be \[d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]

Answer 3

thanks!