A curve C is defined by the parametric equations $x =\frac{m}{1+m}, y = \frac{m^{2}}{1+m}$, where $m$ is not equal to $-1$.
Two distinct points $A$ and $B$ on the curve have parameters a and b respectively. Given that the tangents at $A$ and $B$ intersect the $y$-axis at the same point, show that $a + b = 0$.
After finding $\frac{dy}{dx}$, I can't seem to make any progress on the problem above. Could I make a special request that you not give me the answer but just give me a hint or give me the general direction of the answer; I'd still wanna try to figure this out partially on my own.
Hint: write $\frac{dy}{dx}$ in terms of $m$. Write out the tangent line using the coordinates $x$ and $y$ in $m$. Setting $x=0$ gives you the $y$-intersect. That should give you some equation and Vieta's theorem should end the calculation. Hope I did not spoil the problem.