# Ellipse (S.N.Dey) |Part-7 |Ex-5

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

The ellipse passes through and its eccentricity is find the length of its latus rectum.

Solution.

Since the given ellipse passes through the point , so

Again, the eccentricity of the ellipse is

So, from and we get,

From we get,

So, the length of the latus rectum is

The ellipse passes through the point of intersection of the lines and and its length of latus rectum is find and

Solution.

Two given straight lines are and

From and we get,

From we get,

So, the given ellipse passes through the point

So, the length of latus rectum is

From and we get,

Hence

For Full Solution PDF of the Ellipse ( S N De-Chhaya Mathematics ), click here.

5. The co-ordinates of the centre and of a vertex of an ellipse are and and its eccentricity is find the equation of the ellipse.

Solution.

The centre and the vertex of the ellipse is and respectively.  Since the abscissa of the centre and vertex of the ellipse are equal, the major axis of the ellipse is parallel to -axis. Hence, the equation of the ellipse can be taken in the form

Now, by question, vertex :

Hence by we get the required equation of ellipse

6(i) The vertices of an ellipse are and If the eccentricity of an ellipse be find its equation.

Solution.

Since the ordinates of the two vertices of the ellipse are equal, the equation of the ellipse can be taken in the form :

So, the co-ordinates of the vertices of the ellipse are

From and we get,

Similarly,

Hence, the equation of the ellipse is given by

(ii) Find the equation of the ellipse whose foci are and and whose semi-minor axis  is

Solution.

The co-ordinates of foci of the given ellipse are

So,

The distance between the two foci is

From the co-ordinates of the foci of the ellipse, we can clearly say that the major axis of the ellipse is parallel to the -axis.

So, the equation of the ellipse can be taken in the form :

So, the length of semi-minor axis is unit, so

By we get,

Hence, using we get the required equation of ellipse

(iii) The eccentricity of an ellipse is and the co-ordinates of its one focus and the corresponding vertex are and respectively.  Find the equation of the ellipse . Also find the co-ordinate of the point of intersection of its major axis and the directrix in the same direction.

Solution.

Since the ordinates of the given focus and vertex of the ellipse are equal, hence its major axis is parallel to -axis. Therefore, let us assume that the equation of the required ellipse be

The co-ordinates of one focus and the corresponding vertex of the ellipse are and respectively. By question,

Solving and we get,

So, by we can say that the equation of the ellipse is

2nd Part :

The equation of the major axis :

The directrix of the ellipse :

Hence, the co-ordinates of the point of intersection of its major axis and the directrix in the same direction :

7.  The distance of a point of the ellipse from the centre find the eccentric angle of the point.

Solution.

The equation of the given ellipse is

Any point on the ellipse can be taken as where is the eccentric angle of that point.

Now, since the distance of the point of the  point of the given ellipse from the centre is