Conic Sections — Important Questions
ICSE · Class 11 · Mathematics
62 important questions from Conic Sections for ICSE Class 11 Mathematics, with answers. Part of the ICSE Class 11 Mathematics syllabus.
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Important Questions from Conic Sections
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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