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
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(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