JEE Main asks 1-2 questions on hyperbola annually. Common themes: eccentricity determination (30%), tangent and normal (25%), asymptotes and conjugate hyperbola (20%), rectangular hyperbola (15%), locus problems (10%).

Most common PYQ type: "Find the eccentricity of the hyperbola given [condition]." Conditions include: given relationship between a and b, given latus rectum to transverse axis ratio, given angle between asymptotes, or given a property of tangent/normal.

Second common type: "Find the equation of the hyperbola given [constraints]." Constraints: passes through given points, has given foci and eccentricity, has given asymptotes, or shares foci with a given ellipse.

Common traps: (1) Confusing c^2 = a^2 + b^2 with c^2 = a^2 - b^2 (ellipse formula). This is the most frequent error. (2) For the hyperbola x^2/a^2 - y^2/b^2 = 1, a need not be greater than b (unlike the standard convention for ellipse where a > b). Here a is always associated with the positive term. (3) The tangent condition c^2 = a^2m^2 - b^2 requires a^2m^2 > b^2 for real tangent. Students forget this constraint. (4) The director circle x^2 + y^2 = a^2 - b^2 doesn't exist when a < b. (5) For rectangular hyperbola, confusing xy = c^2 with x^2 - y^2 = a^2. Both are rectangular hyperbolas but have different orientations and parametric forms.

Numerical tip: When the answer involves eccentricity, verify e > 1 for hyperbola. If you get e < 1, recheck your computation.