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consider an ellipse with foci $(x_a,y_a)$ and $(x_b,y_b)$ such that $\sqrt{(x-x_a)^2+(y-y_a)^2}+\sqrt{(x-x_b)^2+(y-y_b)^2}=p$

consider a line parallel to the line through their foci, e.g. $y=\frac{y_b-y_a}{x_b-x_a}x+q$

find the points of intersection

is there a quick way to do this by converting the equation for the ellipse into a conic equation?

cheers, dave xx

human being
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    Bare problem statements like this look like you’re attempting to outsource your coursework and are generally ill-received here. Please update your question with your own efforts at solving the problem (e.g., where specifically are you getting stuck?) or there’s a very good chance that it will simply be closed. From the MSE Tour: “Focus on questions about an actual problem you have faced. Include details about what you have tried and exactly what you are trying to do.” See also How To Ask A Good Question. – amd Nov 04 '19 at 22:14
  • @amd well im not really sure where to start even – human being Nov 04 '19 at 22:16
  • You have a system of two equations in two unknowns. You could grind through a solution directly by, say, substituting for $y$ in the first equation, or, first convert the equation of the ellipse into something easier to work with, such as the general form of a conic equation. To make the latter easier, try transforming to a coordinate system in which the equation of the ellipse is particularly simple. – amd Nov 04 '19 at 22:18
  • Try solving a simpler problem first: what if the foci are at $(\pm c,0)$? – amd Nov 04 '19 at 23:42
  • @amd so i was trying to convert it to 'squished circle' form, is there a good way to do that? is that the right approach? – human being Nov 05 '19 at 00:15

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