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Draw a line through center of ellipse. Given that the center has coords 0,0, what is the coords where the line touches the ellipse?

We know lengths of the two axis, and we know the angle of the line. We can figure out the foci, but I can't see what to do with that information. Hope you can help. Regards.

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1 Answer

Your question doesn't really explain which direction your are drawing the line through the ellipse. But, in general you know that the equation of an ellipse centered at the origin is given by:

(x2/a2) + (y2/b2) = 1


a = radius on the x axis

b = radius on the y axis

Assuming you are drawing your line on either of the axes then the answer becomes

(x2/a2) + (02/b2) = 1

x2 = a2

x = ±√(a2)

So it's (-a,0) and (a,0) if the line is drawn on the x axis

(02/a2) + (y2/b2) = 1

y2 = b2

y = ±√(b2)

or (0,-b) and (0,b) if the line is drawn on the y axis

If your problem is asking for a general equation  (any line through the center) then the solution obviously becomes more complex; hopefully this is sufficient for your assignment. Best of luck to you.