Michael B. answered • 04/13/13

Seasoned and experienced tutor with extensive science background

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.