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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).