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.

8. is any double ordinate of the ellipse
; find the equation to the locus of the point of trisection of
that is nearer to
Solution.
Let
Suppose that the point is the nearest point of
which is the point of trisection of
i.e.,
Hence, from we get the locus of the point which is
For Full Solution PDF of the Ellipse (S N De-Chhaya Mathematics), click here.
9. Show that the double ordinate of the auxiliary circle of an ellipse passing through the focus is equal to the minor axis of the ellipse.
Solution.

Let the equation of the ellipse be
and the auxiliary circle of is
Suppose that is the double ordinate of the auxiliary circle
Now, the equation of is given by
Since passes through the focus i.e.,
, so
Since the auxiliary circle has double ordinate,
Note[*] :
10. is the centre of an ellipse whose semi-minor axis is
The ordinate of a point
of the ellipse intersects its auxiliary circle at
(when produced). The straight line through
drawn parallel to
cuts the major axis at
Prove that,
Solution.

Let the equation of the ellipse be
Clearly, and
are similar triangle,
11. If and
are the eccentric angles of the points
and
respectively on the ellipse
, show that the equation of the chord
is
Solution.
Since are the eccentric angles of the points
and
respectively, so
The equation of
is
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