Hyperbola2 questions2 PYQ

Hyperbola — JEE Maths Practice Questions & Solutions

2 questions on Hyperbola with full step-by-step solutions, including past-year (PYQ) problems. Free to practice.

mediumPYQ · JEE Main 2026
Let the eccentricity ee of a hyperbola satisfy 6e2−11e+3=06e^2-11e+3=0. If the foci are (3,5)(3,5) and (3,−4)(3,-4), then the length of its latus rectum is:
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mediumPYQ · JEE Main 2026
Let H:x2a2−y2b2=1H:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1 be a hyperbola such that the distance between its foci is 66 and the distance between its directrices is 83\dfrac83. If the line x=αx=\alpha intersects HH at AA and BB such that the area of △AOB\triangle AOB is 4154\sqrt{15}, where OO is the origin, then α2\alpha^2 equals
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