JEE Main 2022 — Hyperbola Questions with Solutions

Let the eccentricity of the hyperbola x 2 a 2 - y 2 b 2 = 1 be 5 4 . If the equation of the normal at the point 8 5 , 1…

Let the tangent drawn to the parabola y 2 = 24 x at the point α , β is perpendicular to the line 2 x + 2 y =…

Let the equation of two diameters of a circle x 2 + y 2 - 2 x + 2 f y + 1 = 0 be 2 p x - y = 1 and 2 x + p y = 4 p . Th…

Let the hyperbola H : x 2 a 2 - y 2   b 2 = 1 pass through the point 2 2 , - 2 2 . A parabola is drawn whose focus…

Let the hyperbola H : x 2 a 2 - y 2 = 1 and the ellipse E : 3 x 2 + 4 y 2 = 12 be such that the length of latus rectum…

If the line x - 1 = 0 , is a directrix of the hyperbola k x 2 - y 2 = 6 , then the hyperbola passes through the point

For the hyperbola H : x 2 - y 2 = 1 and the ellipse E : x 2 a 2 + y 2 b 2 = 1 , a > b > 0 , let the (1) eccentr…

Let the foci of the ellipse x 2 16 + y 2 7 = 1 and the hyperbola x 2 144 - y 2 α = 1 25 coincide. Then the length…

Let a > 0 ,   b > 0 . Let e and l respectively be the eccentricity and length of the latus rectum of the h…

Let H : x 2 a 2 - y 2   b 2 = 1 , a > 0 ,   b > 0 , be a hyperbola such that the sum of lengths of th…