# Ellipse (S.N.Dey) |Part-8 |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.

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 