jee_main_2025_07_april_evening - Conic Sections Topics

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QUESTION #62 Properties of Ellipse
Let the length of a latus rectum of an ellipse (x²)/(a²) + (y²)/(b²) = 1 be 10. If its eccentricity is the minimum value of the function f(t) = t² + t + (11)/(12), t in R, then a² + b² is equal to:
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QUESTION #68 Eccentricity and Foci
Let e₁ and e₂ be the eccentricities of the ellipse x²b² + y²25 = 1 and the hyperbola x²16 - y²b² = 1, respectively. If b < 5 and e₁e₂ = 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 (α,2√(5)) on the hyperbola is p, then 4p is equal to
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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

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