Is there any method to find the common chord of $2$ intersecting parabolas $?$
I was told that equation of common chord of two parabolas is $S_1-S_2$ where $S_1$ and $S_2$ are equations of the parabolas, which does not seems to work in every case. So can any body help me out. Thanks in advance.
You would need to start by finding the x-coordinates of their intersections, i.e. the points where $P_1 = P_2$. In other words, you need to solve the equation $P_1 - P_2 = 0$ which may be where the idea of subtracting the equations came from. Once you've solved that equation for x, you can use either equation to find the corresponding y values. At that point, you've got two (x, y) pairs and the equation of the chord will be the equation through those points.