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jee_main_2025_07_april_evening - Conic Sections Topics

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Sample Questions in this Chapter

QUESTION #62 Properties of Ellipse
Let the length of a latus rectum of an ellipse fracx^2a^2 + fracy^2b^2 = 1 be 10. If its eccentricity is the minimum value of the function f(t) = t^2 + t + frac1112, t in mathbfR, then a^2 + b^2 is equal to:
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QUESTION #68 Eccentricity and Foci
Let mathbfe_1 and mathbfe_2 be the eccentricities of the ellipse fracmathrmx^2mathrmb^2 + fracmathrmy^225 = 1 and the hyperbola fracmathrmx^216 - fracmathrmy^2mathrmb^2 = 1, respectively. If mathrmb < 5 and mathrme_1mathrme_2 = 1, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is:
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QUESTION #74 Properties of Hyperbola
Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and one focus and the corresponding directrix of this hyperbola be (-5,0) and 5x + 9 = 0, respectively. If the product of the focal distances of a point (alpha,2sqrt5) on the hyperbola is p, then 4p is equal to
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