Question

Find the equation of the ellipse whose axes are along the coordinate axes, vertices are (± 5,0) and foci at (± 4,0).

Answer 1

Since the vertices are (5, 0) and foci at (4, 0), the equation of the major axis is y = 0, i.e. x-axis. [Recall the major axis contains both the foci and both the vertices.]Since, centre of the ellipse is the mid-point of the vertices (or foci), it is (0, 0), the originin the present case. Therefore the minor axis (theone passing through the centre and perpendicular to the major axis) is x = 0, i.e. y-axis.Therefore, an equation if the ellipse must be of the form ----------------(1)We have a = 5, ae = 4, therefore. Also.Substituting these values in (1), we get the equation of required ellipse as