What did you do to try and prove the statements? Hint: at the x-intercept y=0.
Suppose that the circle
x^2 + 2Ax + y^2 + 2By = C has two x-intercepts, xsub1 and xsub2 and two y-intercepts, ysub1 and ysub2. Prove each statement.
(a) (xsub1+xsub2)/(ysub1+ysub2) equals A/B
(b) (xsub1)(xsub2) - (ysub1)(ysub2) = 0
(c) (xsub1)(xsub2)+(ysub1)(ysub2) = -2C
At the x-intercept when y=0 the two points are (x_{1},0) and (x_{2},0).
Putting y=0 into the equation of the circle you get x^{2}+2Ax-C=0
Solving this quadratic equation for x you get
Therefore, and
That should be enough to get you started