Conic Sections – Ellipse (Standard Equations & Properties)

Grade 11 Maths — Conic Sections – Ellipse (Standard Equations & Properties): 25 practice questions with instant scoring and explanations.

1. The standard equation of an ellipse with foci on the x-axis is:
2. For the ellipse x²/25 + y²/16 = 1, the length of the major axis is:
3. If the equation of an ellipse is x²/9 + y²/4 = 1, then the eccentricity is:
4. The foci of the ellipse x²/36 + y²/20 = 1 are located at:
5. For an ellipse x²/a² + y²/b² = 1 where a > b, the relationship between a, b, and c is:
6. The eccentricity of an ellipse is:
7. If the eccentricity of an ellipse is 3/5 and the semi-major axis is 10, then the semi-minor axis is:
8. The sum of distances from any point on the ellipse to the two foci is:
9. For the ellipse 4x² + 9y² = 36, the length of the minor axis is:
10. The equations of directrices for the ellipse x²/a² + y²/b² = 1 (where a > b) are:
11. For the ellipse x²/16 + y²/9 = 1, the latus rectum length is:
12. An ellipse has semi-major axis 13 and semi-minor axis 12. Its eccentricity is:
13. The distance between the two directrices of the ellipse x²/25 + y²/9 = 1 is:
14. If a point (3, 2) lies on the ellipse and the eccentricity is 1/2, which is the ellipse equation?
15. The auxiliary circle of an ellipse x²/a² + y²/b² = 1 has equation:
16. For the ellipse x²/25 + y²/16 = 1, the major axis is along:
17. The parametric equations of ellipse x²/a² + y²/b² = 1 are:
18. If the ellipse equation is x²/25 + y²/9 = 1 with c = 4, then e equals:
19. The eccentricity of the ellipse 9x² + 16y² = 144 is:
20. For an ellipse, if the sum of focal distances from a point is 20, then 2a equals:
21. The focal chord perpendicular to major axis of x²/9 + y²/4 = 1 has length:
22. If 2a = 10 and 2b = 8 for an ellipse, then 2c equals:
23. The equation x²/25 + y²/9 = 1 has major axis length:
24. For the ellipse x²/a² + y²/b² = 1, if e = √3/2, then a/b equals:
25. The vertices of x²/16 + y²/9 = 1 are: