# Ellipse (S.N.Dey) | Part-3 | Ex-5

###### In the previous article , we solved few solutions of Short Answer Type Questions of Ellipse Chapter of  S.N.Dey mathematics, Class 11. In this chapter, we will solve few more.

4(i) Find the lengths of axes  of the ellipse whose eccentricity is and the distance between focus and directrix is

Solution.

The distance between focus and directrix

By question,

Hence, the length of the major axis and the length of the minor axis

and are two foci of an ellipse whose eccentricity is Find the length of the major axis.

Solution.

Eccentricity

The distance between the two given foci is

Hence, the length of the major axis

5. The length of the latus rectum of an ellipse is unit and that of the major axis, which lies along the axis , is unit. Find its equation in the standard form . Determine the co-ordinates of the foci and the equations of its directrices.

Solution.

The length of the latus rectum of the ellipse is given by

Again, the length of the major axis (2a) is given by

Hence,the equation of the ellipse is

The eccentricity of the ellipse is given by

The co-ordinates of the foci of the ellipse is given by

The equation of the directrix is given by

6. Taking major and minor axes along and axes, find the equation of the ellipse whose

co-ordinates of foci are and the length of minor axis is

Solution.

Since the foci of the given ellipse lie on the -axis , the major axis of the ellipse lies on the axis.

Again, the centre of the ellipse is given by i.e.

So, the ellipse is of the form

So, the co-ordinates of the foci

The length of the minor axis is given by

Hence, using , the equation of the ellipse is

eccentricity and the length of latus rectum

Solution.

Length of latus rectum

From and we get,

So, the equation of the ellipse is

length of minor axis is and the distance between the foci is

Solution.

By the condition, length of minor axis is given by

The distance between the foci is

Hence, the equation of the ellipse is given by

co-ordinates of one vertex are and the co-ordinates of one end of minor axis are

Solution.

By question, the equation of the ellipse can be taken as

Co-ordinates of one vertex is and co-ordinates of one end of minor axis is

Hence, by we get,

co-ordinates of foci are and the eccentricity is

Solution.

By question, the co-ordinates of foci

Hence, the equation of the ellipse is

Find the equation of the ellipse whose

eccentricity is focus is and directrix is

Solution.

Let be any point on the ellipse . The co-ordinates of the focus : and the equation of the directrix is given by

Now, the length of the perpendicular from P on the straight line (1) is given by

Now, for the ellipse, we have

Hence, the equation of the ellipse is given by

eccentricity is focus is and directrix is

Solution.

Let be any point on the ellipse. The co-ordinates of the focus :

The equation of the directrix is

The length of the perpendicular from P on the straight line (1) is

Now, for the ellipse

Hence, the equation of the ellipse is

eccentricity is focus is directrix is

Solution.

Let be any point on the ellipse. The co-ordinates of focus :   The equation of the directrix :

The perpendicular distance of the point P from the straight line (1) is

Now, for the ellipse, we know that

focus is directrix is and eccentricity is

Solution.

Let be any point on the ellipse. The co-ordinates of focus :   The equation of the directrix :

The perpendicular distance of the point P from the straight line (1) is

Now, for the ellipse, we know that

Hence, the equation represents the required ellipse.