# Lecture 4 Ellipse Conic Sections Class 11 Maths

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# Lecture - 4 Chapter 11 Conic Sections

Explanation of all basic details of standard ellipse, method to remember their rules

 NCERT Exercise 11.3

In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

Question 1.  $\frac{x^2}{36}+\frac{y^2}{16}=1$
Question 2. $\frac{x^2}{4}+\frac{y^2}{25}=1$
Question 3. $\frac{x^2}{16}+\frac{y^2}{9}=1$
Question 4. $\frac{x^2}{25}+\frac{y^2}{100}=1$
Question 5. $\frac{x^2}{49}+\frac{y^2}{36}=1$
Question 6. $\frac{x^2}{100}+\frac{y^2}{400}=1$
Question 7. $36x^2+4y^2=144$
Question 8. $16x^2+y^2=16$
Question 9. $4x^2+9y^2=36$

In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions:

Question 10. Vertices (± 5, 0), foci (± 4, 0)
Question 11. Vertices (0, ± 13), foci (0, ± 5)
Question 12. Vertices (± 6, 0), foci (± 4, 0)
Question 13. Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)
Question 14. Ends of major axis $(0, \pm \sqrt{5})$, ends of minor axis (± 1, 0)
Question 15. Length of major axis 26, foci (± 5, 0)
Question 16. Length of minor axis 16, foci (0, ± 6).
Question 17. Foci (± 3, 0), a = 4
Question 18. b = 3, c = 4, center at the origin; foci on the x axis.
Question 19. Center at (0,0), major axis on the y-axis and passes through the points (3, 2) and (1, 6).
Question 20. Major axis on the x-axis and passes through the points (4, 3) and (6, 2).