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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).