JEE Main 2023 — Hyperbola Questions with Solutions

Let H be the hyperbola, whose foci are 1 ± 2 , 0 and eccentricity is 2 . Then the length of its latus rectum is:

Let m 1 and m 2 be the slopes of the tangents drawn from the point P 4 , 1 to the hyperbola H : y 2 25 - x 2 16 = 1 If…

Let the tangent to the parabola y 2 = 12 x at the point 3 ,   α be perpendicular to the line 2 x + 2 y = 3 .…

Let P x 0 , y 0 be the point on the hyperbola 3 x 2 - 4 y 2 = 36 , which is nearest to the line 3 x + 2 y = 1 . Then 2…

If the maximum distance of normal to the ellipse x 2 4 + y 2 b 2 = 1 , b < 2 , from the origin is 1 , then the ecce…

The vertices of a hyperbola H are ± 6 , 0 and its eccentricity is 5 2 . Let N be the normal to H at a point in the…

Let R be a rectangle given by the lines x = 0 ,   x = 2 , y = 0 and y = 5 . Let A α , 0 and B 0 , β , &#…

The foci of a hyperbola are ( ± 2 , 0 ) and its eccentricity is 3 2 . A tangent, perpendicular to the line 2 x + 3…

Let H n : x 2 1 + n - y 2 3 + n = 1 ,   n ∈ ℕ . Let k be the smallest even value of n such that the ec…

Let the eccentricity of an ellipse x 2 a 2 + y 2 b 2 = 1 is reciprocal to that of the hyperbola 2 x 2 - 2 y 2 = 1 . If…