jee_main_2025_03_april_morning - Conic Sections Topics

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QUESTION #0 Ellipse and Line Properties
A line passing through the point P(√(5), √(5)) intersects the ellipse (x²)/(36) + (y²)/(25) = 1 at A and B [cite: 567] such that (PA) · (PB) is maximum. Then 5(PA² + PB²) is equal to
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QUESTION #68 Common Tangents and Shortest Distance
The radius of the smallest circle which touches the parabolas y = x² + 2 and x = y² + 2 is[cite: 673]:
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QUESTION #72 Hyperbola Properties
Let the product of the focal distances of the point P(4, 2√(3)) on the hyperbola H : (x²)/(a²) - (y²)/(b²) = 1 be 32[cite: 690, 691]. Let the length of the conjugate axis of H be p and the length of its latus rectum be q[cite: 692]. Then p² + q² is equal to[cite: 693]:
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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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