Question

A circle has a diameter with endpoints (-10, -6) and (-2, -4).
What is the equation of the circle?

Answer 1

(x-x1)(x-x2) + (y-y1)(y-y2) =0

Answer 2

where (x1,y1) and (x2,x2) are given end points of a diameter

Answer 3

r2 = (x + 4)2 + (y + 5)2
r2 = (x + 6)2 + (y + 5)2
r2 = (x + 4)2 + (y + 1)2
or
r2 = (x + 6)2 + (y - 1)2
are my only answer options

Answer 4

The answers are not adequate because r^2 is not given.
In a case like this, you may be better off finding the centre of the circle and use the standard equations.
The centre of the circle is given by the mid-point between the two given points:
\((xm,ym)=((xa+xb)/2, (ya+yb)/2)\)
The equation of the circle is then
\((x-xm)^2+(y-ym)^2 = r^2\)
whatever r=radius may be.

Answer 5

ok thanks