CBSE - Class 11 Mathematics Conic Sections Worksheet
EXERCISE 10.3
1.
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. 3. $frac{x^2}{16} + $frac{y^2}{9} = 1$
2.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 20. Major axis on the $x$-axis and passes through the points (4,3) and (6,2).
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. 2. $frac{x^2}{4} + $frac{y^2}{25} = 1$
4.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 10. Vertices (± 5, 0), foci (± 4, 0)
5.
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. 9. 4$x^2$ + 9$y^2$ = 36
6.
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. 1. $frac{x^2}{36} + $frac{y^2}{16} = 1$
7.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 17. Foci (± 3, 0), $a$ = 4
8.
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. 6. $frac{x^2}{100} + $frac{y^2}{400} = 1$
9.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 18. $b$ = 3, $c$ = 4, centre at the origin; foci on the $x$ axis.
10.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 15. Length of major axis 26, foci (± 5, 0)
11.
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. 5. $frac{x^2}{49} + $frac{y^2}{36} = 1$
12.
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. 4. $frac{x^2}{25} + $frac{y^2}{100} = 1$
13.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 16. Length of minor axis 16, foci (0, ± 6).
14.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 12. Vertices (± 6, 0), foci (± 4, 0)
15.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 13. Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)
16.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 11. Vertices (0, ± 13), foci (0, ± 5)
17.
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. 7. 36$x^2$ + 4$y^2$ = 144
18.
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. 8. 16$x^2$ + $y^2$ = 16
19.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 14. Ends of major axis (0, ±$sqrt{5}$ ), ends of minor axis (± 1, 0)
20.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 19. Centre at (0,0), major axis on the $y$-axis and passes through the points (3, 2) and (1,6).