Lecture-4

Conic Sections Lecture 4
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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).