JEE Main 2025 — Hyperbola Questions with Solutions

Let the circle C touch the line x-y+1=0, have the centre on the positive x -axis, and cut off a chord of length 4√(13)…

Let the product of the focal distances of the point P(4,2 √(3)) on the hyperbola H: x²a²-y²~b²=1 be 32 . Let the length…

Let E: x²a²+y²~b²=1, a and H: x²~A²-y²~B²=1. Let the distance between the foci of E and the foci of H be 2 √(3). If a-A…

Let the sum of the focal distances of the point P(4,3) on the hyperbola H: x²a²-y²~b²=1 be 8 √((5)/(3)). If for H, the…

Let one focus of the hyperbola H: x²a²-y²~b²=1 be at (√(10), 0) and the corresponding directrix be x=9√(10). If e and l…

If the equation of the hyperbola with foci (4,2) and (8,2) is 3 x²-y²-α x+β y+γ=0, then α+β+γ is equal to _____.

Let e₁ and e₂ be the eccentricities of the ellipse x²~b²+y²25=1 and the hyperbola x²16-y²~b²=1, respectively. If b 5 an…

Let the foci of a hyperbola be (1,14) and (1,-12). If it passes through the point (1,6), then the length of its latus-r…

Consider the hyperbola (x²)/(a²)-(y²)/(b²)=1 having one of its focus at P(-3,0). If the latus ractum through its other…

Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and on…