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.

## 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?

# 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:

(x^{2}/a^{2}) + (y^{2}/b^{2}) = 1

Where

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

(x^{2}/a^{2}) + (0^{2}/b^{2}) = 1

x^{2} = a^{2}

x = ±√(a^{2})

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

(0^{2}/a^{2}) + (y^{2}/b^{2}) = 1

y^{2} = b^{2}

y = ±√(b^{2})

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.