# Thread: Prove Each Statement

1. ## Prove Each Statement

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

2. ## Re: Prove Each Statement

What did you do to try and prove the statements? Hint: at the x-intercept y=0.

3. ## Re: Prove Each Statement

Can you at least get me started by proving part (a)?

4. ## Re: Prove Each Statement

At the x-intercept when y=0 the two points are (x1,0) and (x2,0).
Putting y=0 into the equation of the circle you get x2+2Ax-C=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