Conic Sections — Practice Quiz
ICSE · Class 11 · Mathematics
Try a 4-question quiz on Conic Sections for ICSE Class 11 Mathematics: tap an answer to check it and see why. 62 questions in the full chapter test.
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Quick Quiz: Conic Sections
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Find the eccentricity of the ellipse x^2/25 + y^2/16 = 1.
For the ellipse 16x^2 + 25y^2 = 400, find PF1 + PF2 for any point P on the ellipse.
Find the equation of the ellipse whose foci are (-2, 4) and (4, 4) and whose length of major axis is 10.
Find the equation of the parabola whose vertex is (0, 0) and focus is (3, 0).
Sample Questions
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.
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.
For the hyperbola x^2/16 - y^2/9 = 1, find its eccentricity.
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5/4
Here a^2 = 16 and b^2 = 9. So c = √(a^2 + b^2) = √(25) = 5. Then e = c/a = 5/4.
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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