JEE Main Maths Ellipse and Hyperbola Previous Year Questions

JEE Main Ellipse and Hyperbola PYQ, free to download as a 41-page PDF. The bank carries 27 solved questions from the 2021 to 2026 papers and takes roughly two days to work through, so split it across ellipse and hyperbola.

Questions run newest year first, with the options exactly as printed. The answer key follows, then a worked solution for each one.

JEE Main Ellipse and Hyperbola Weightage

Conic sections is one of the largest chapters in JEE Main Mathematics, and ellipse and hyperbola together contribute roughly two to four questions per session. This set excludes circle and parabola, which are their own chapters.

Five or six a year is the steady rate, which makes this one of the more predictable chapters to prepare in the paper.

What the 27 Questions Cover

• Chords with a given midpoint, the single most repeated idea here, solved through the relation T equals S one
• Tangency conditions, including the sign difference between the ellipse and hyperbola forms
• Normals, and the point through which a given normal passes
• Focal distances and latus rectum, recovered from eccentricity and geometry
• Mixed-curve questions, where one line touches both a hyperbola and a parabola
• Optimisation, such as the largest circle inscribed in an ellipse or the maximum area of a triangle

Formulas Worth Memorising

• Tangency: c squared equals a squared m squared plus b squared for an ellipse, minus b squared for a hyperbola
• Midpoint chord: T equals S one, with the midpoint substituted in
• Chord length: the difference of the roots times the root of one plus m squared
• The normal carries a plus sign between its terms where the tangent carries a minus

How to Approach the Set

For any midpoint chord, write T equals S one and substitute the midpoint. It turns what looks like a geometry problem into one line of algebra, and it is the most repeated idea in the chapter.

For a chord length, use the difference of the roots rather than finding both endpoints. Solving for two intersection points and then applying the distance formula works, but it takes three times as long under exam conditions.

Where two tangents meet at the ends of a chord, that intersection is the pole of the chord. Comparing coefficients against the polar is far quicker than writing out both tangents and solving them together.

Common Mistakes

• Using the ellipse tangency condition on a hyperbola, which flips a sign and changes the answer
• Copying the tangent's minus sign into the normal, which has a plus
• Listing quadrilateral vertices in the order given rather than in cyclic order
• Stopping at the first option that satisfies an equation when the question asks which one does not
• Forgetting that a minimising parameter must still lie within its own allowed range

Two to Solve First

The 2026 question about the line that misses the hyperbola. Substituting the line and forcing a negative discriminant reduces the whole thing to the clean condition that c squared plus one is less than nine m squared. Three of the four options sit just below the resulting bound, so the algebra has to be exact.

Then the 2022 question that feeds a parabola tangent into a hyperbola normal. A perpendicularity condition fixes a point on a parabola, that point defines a hyperbola, and you are asked which of four points does not lie on its normal. Three options satisfy the equation, so finding one that works is not yet an answer.

Video Solutions

Source: JEE Wallah

Using the Answer Key

Do the set in two timed sittings, allowing about three minutes a question. Mark the key in one pass, right or wrong only, then read the solution for every miss and every lucky guess. Each opens with a one-line quick solution you can stop at and retry from.

For the rest of the paper, the JEE Main Inverse Trigonometric Functions PYQs cover that chapter in the same format.