How do you write an equation of an ellipse in standard form with foci (8, 0) and (-8, 0) if the minor axis has y-intercepts of 2 and -2?
Use x- and y-intercepts to deduce standard form ellipse coefficients. Deduce x-intercepts from distance from the foci to known points.
We can see from the symmetry of the given points that this ellipse is centred at
A definition of an ellipse is the set of points the sum of whose distances from the two foci is a constant. We can from the given information deduce that distance sum - the distance from both foci to either y-intercept is
Let the positive x-intercept be at