Suppose I have 2 different conics - for example, a circle and a parabola. How do I find the common chord between them? I tried implementing the $S_1-S_2=0$ approach, but it is not giving me any proper answers, as it results in equations like $x^2+6x-4y=0$, which I have no idea how to obtain the common chord from.
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Hint...try $$S_1-\lambda S_2=0$$ and choose $\lambda$ so the non-linear terms vanish
David Quinn
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what about equations like $y^2=8x$ and $x^2+y^2-2x-4y=0$? – Siddharth Venu Mar 25 '17 at 21:02
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Maybe you could edit your question so that you are specifically asking about this particular situation. These curves intersect at the origin, so you can put $y=mx$ and solve in both equations to get $m=2$ – David Quinn Mar 25 '17 at 21:27