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Conic Sections

ICSE · Class 11 · Mathematics

Practice quiz for Conic Sections — ICSE Class 11 Mathematics. MCQs and questions with answers to test your preparation.

62 questions26 flashcards5 concepts

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A 3D diagram illustrating how different conic sections (circle, ellipse, parabola, hyperbola) are formed by the intersection of a plane with a double-napped right circular cone at various angles.
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Quick Quiz: Conic Sections

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1

Find the eccentricity of the ellipse x^2/25 + y^2/16 = 1.

2

For the ellipse 16x^2 + 25y^2 = 400, find PF1 + PF2 for any point P on the ellipse.

3

Find the equation of the ellipse whose foci are (-2, 4) and (4, 4) and whose length of major axis is 10.

4

Find the equation of the parabola whose vertex is (0, 0) and focus is (3, 0).

62 Questions·
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Sample Questions

1multiple choice
3 marks

For the parabola y^2 = 8x, find the coordinates of a point whose focal distance is 4 units.

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(2, 4) and (2, -4)

The parabola y^2 = 8x is y^2 = 4ax, so a = 2. Its focus is (2, 0). Let the point be (x, y). Focal distance 4 gives (x - 2)^2 + y^2 = 16. Since the point lies on the parabola, y^2 = 8x. Substituting gives (x - 2)^2 + 8x = 16, so x^2 + 4x - 12 = 0, giving x = 2 or -6. Only x = 2 fits the parabola. Then y^2 = 16, so y = ±4.

2multiple choice
3 marks

Find the directrix of the parabola whose vertex is (-3, 0) and directrix is x + 5 = 0?

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x = -5

The directrix is already given by x + 5 = 0, which simplifies to x = -5.

3multiple choice
3 marks

For the hyperbola x^2/16 - y^2/9 = 1, find its eccentricity.

Show answer

5/4

Here a^2 = 16 and b^2 = 9. So c = √(a^2 + b^2) = √(25) = 5. Then e = c/a = 5/4.

4multiple choice
3 marks

Find the length of the latus rectum of the hyperbola x^2/36 - y^2/64 = 1.

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64/3

Here a = 6 and b = 8. The latus rectum length is 2b^2/a = 2(64)/6 = 64/3.

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Frequently Asked Questions

What are the important topics in Conic Sections for ICSE Class 11 Mathematics?
Key topics in Conic Sections include Conic Sections Classification, Conic Sections Overview, Conic Sections Overview. These are the concepts ICSE Class 11 examiners draw on most — study them first, then practise related questions.
How to score full marks in Conic Sections — ICSE Class 11 Mathematics?
Understand the core concepts first, then work through the 62 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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