Write the equation for the circle whose diameter has endpoints at (4,9/2) and (0,-5/2)

Question

Write the equation for the circle whose diameter has endpoints at (4,9/2) and (0,-5/2)

Answer 1

The centre will be the midpoint of the diameter so ( (4+0)/2, (9/2 + -5/2) / 2) so (2, 1)

The radius will be the distance from the centre to one of the given points so

√ ( 4-2)^2 + (9/2 - 1 )^2 = √ 4 + (7/2)^2 = √ 65/4 = √65 / 2

so r² = 65 / 4 [ The answer given by Mark above is incorrect ]

So the equation will be (x - 2) ^2 + (y-1) ^ 2 = (65/4)

You can check this by graphing on Desmos or a TI-84. (which I just did)

Answer 2

Draw and label a diagram!

C(2, 1)

r² = 10.25

Use the graphing form of the equation and answer.