
Prove Each Statement
Suppose that the circle
x^2 + 2Ax + y^2 + 2By = C has two xintercepts, xsub1 and xsub2 and two yintercepts, 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

Re: Prove Each Statement
What did you do to try and prove the statements? Hint: at the xintercept y=0.

Re: Prove Each Statement
Can you at least get me started by proving part (a)?

Re: Prove Each Statement
At the xintercept 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}+2AxC=0
Solving this quadratic equation for x you get $\displaystyle x=\frac{2A\pm \sqrt{(2A)^2+4C}}{2}=\frac{2A\pm \sqrt{4(A^2+C)}}{2}=\frac{2A\pm 2\sqrt{A^2+C}}{2}$
$\displaystyle x=A\pm \sqrt{A^2+C}$
Therefore, $\displaystyle x_1=A+ \sqrt{A^2+C}$ and $\displaystyle x_2=A \sqrt{A^2+C}$
That should be enough to get you started