###### 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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