JEE Main Maths Ellipse and Hyperbola Previous Year Questions

JEE Main Ellipse and Hyperbola PYQ, free to download as a 40-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.

Every question keeps the year it was asked and the options exactly as printed. An answer key follows the questions, then a full worked solution for all 27.

How the Answers Were Checked

These questions come from our tagged JEE Main bank, which ships an answer key. That key was not taken on trust.

Every one of the 27 answers was independently re-derived from the question itself before publication, and all 27 agreed with the bank. Where a question had two defensible readings, the solution says which one the option list supports.

What the 27 Questions Cover

Ellipse and hyperbola sit inside Conic Sections, one of the largest chapters in JEE Main Mathematics. This set deliberately excludes circle and parabola questions, which belong to their own chapters.

• 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 the 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

The Five Moves That Solve Almost All of Them

Across the 27 questions the same handful of moves keeps working. Naming them makes the chapter much faster.

• For any midpoint chord, write T equals S one and substitute the midpoint; it turns the question into one line of algebra
• The tangency condition is c squared equals a squared m squared plus b squared for an ellipse and minus b squared for a hyperbola
• For a chord length use the difference of the roots times the root of one plus m squared, rather than finding both endpoints
• The normal to a conic carries a plus sign between its terms where the tangent carries a minus
• The intersection of tangents at the ends of a chord is the pole of that chord, so compare coefficients instead of writing two tangents

Two Questions Worth Doing First

If time is short, start here. Each teaches a move the rest of the set reuses.

2026, the line that misses the hyperbola. Substituting the line and forcing a negative discriminant reduces the whole question 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.

2022, tangent to a parabola feeding a hyperbola normal. A perpendicularity condition fixes a point on a parabola, that point defines a hyperbola, and the question then asks 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.

Watch Ellipse and Hyperbola Solved for JEE Main

Source: JEE Wallah

How to Use the Answer Key and Solutions

Attempt the whole set before checking anything. The layout is built so an answer cannot be glimpsed by accident.

• Do the set in two timed sittings, allowing about three minutes a question
• Mark the answer key in one pass, right or wrong only
• Read the solution for every miss and every lucky guess
• Each solution opens with a one-line quick solution, so you can stop there and retry

Traps These Questions Are Built Around

A handful of errors account for most lost marks here, and several questions exist only to catch them.

• 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