NCERT Exemplar Solutions Class 11 Maths Chapter 10 Conic Sections

Conic Sections is the chapter where a single wrong reading of a denominator changes the whole answer. The NCERT Exemplar Solutions for Class 11 Maths Chapter 10 Conic Sections on this page solve all 59 questions of the chapter, step by step, according to the 2026-27 NCERT Exemplar.

Every solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT Exemplar, and checked line by line against the official answer key.

One numbering note before students start. The NCERT Exemplar book prints Conic Sections as its Chapter 11, and the exercise is numbered Exercise 11.3. In the current NCERT textbook order it is Chapter 10, which is the number used on this page. The questions are identical. The solutions PDF runs to 228 pages.

• 59 questions solved: Short Answer, Long Answer, True/False, Fill in the Blanks and Multiple Choice.
• Three errors in the printed key flagged: Q27, Q32(a) and Q49, each with the one-line check that settles it.
• Exam focus: useful for CBSE Boards, JEE Main, JEE Advanced and CUET.

Topics Covered in the Class 11 Maths Conic Sections Exemplar

The Conic Sections Exemplar works through all four curves, but it spends most of its questions on the circle and the ellipse. Very few questions hand students a standard equation directly. Most give a geometric condition, such as a tangent, a chord or a focal distance, and expect the equation to be built from it. These are the topics the 59 questions are built on.

• Circles from conditions: circles that touch both axes, touch a given line, or have a centre pinned to a line such as y = x − 1.
• Tangents and chords: the perpendicular distance from the centre as the tangency test, and the half-chord Pythagoras step.
• Position of a point: deciding inside, on, or outside a circle before computing any distance.
• Parabola: vertex, focus and directrix, the four standard forms, focal distance and latus rectum.
• Ellipse: eccentricity, foci, directrices, latus rectum and the sum of focal distances 2a.
• Hyperbola: c² = a² + b², eccentricity greater than 1, and the difference of focal distances.
• Focus-directrix definition: building a conic from SP = e × PM when the directrix is a slanted line.

Important: for an ellipse, a is the larger semi-axis. For a hyperbola, a is decided by which term is positive, not by which number is larger. Students who carry the ellipse habit into Q21 get an eccentricity below 1, which is impossible for a hyperbola.

Exercise 11.3 Question-Type Breakdown for Conic Sections

All 59 questions sit inside the single exercise the book prints as Exercise 11.3, grouped by format. The table below shows how the exercise splits, so students can plan practice by question type rather than solving straight through.

The Long Answer block (Q23 to Q32) is where the chapter is won or lost. It holds the locus derivations in Q29 to Q31 and both of the multi-answer traps, Q27 and Q32. The Short Answer block is the largest group and is best split across two sittings, because Q1 to Q10 are circles and Q11 to Q22 move through the ellipse, parabola and hyperbola.

Three Errors in the Printed Conic Sections Exemplar Key Every Student Must Know

The printed NCERT Exemplar key for this chapter has three questions where students cannot simply trust what is printed. They are not the same kind of error, so they are listed separately below. One key is incomplete, one key row is wrong, and one question has an option list in which no option works. Each is settled by a check students can run in a few seconds.

Q27 has two circles, not one. The question asks for a circle of radius 3 through (7,3) with its centre on y = x − 1. Putting the centre at (h, h−1) and using the radius condition gives h² − 11h + 28 = 0, which factorises as (h−4)(h−7) = 0. Both roots are real, so both centres, (4,3) and (7,6), give a genuine circle of radius 3 through (7,3). The key prints only the first. The Exemplar itself settles this: Solved Example 20 of the same chapter poses the identical problem and prints both equations. A quadratic with a positive discriminant does not have one answer.

Q32(a) is a key row printed against the wrong question. The key gives 15x² − y² = 15, which is the answer to Q31. The check takes one line. Written in standard form, 15x² − y² = 15 is x²/1 − y²/15 = 1, so a = 1 and c = 4, giving vertices (±1, 0) and foci (±4, 0). Q32(a) asks for vertices (±5, 0) and foci (±7, 0), which the printed curve matches on neither count. The correct answer is x²/25 − y²/24 = 1, where c² = 25 + 24 = 49 gives foci at (±7, 0) exactly as asked.

Q49 has no correct option. The question asks for the circle with centre on the y-axis passing through the origin and (2,3). Those two conditions force the form x²+y²+2fy = 0, and the point (2,3) then gives 3x²+3y²−13y = 0 uniquely. Substituting (2,3) into each printed option makes every one of them fail, including the key's (C). The mathematics is not in doubt, only the printing is. In an exam, students should write the correct circle, show the substitution that rules out each option, and mark (C) while noting the misprint. Never select an option you have just proved false without saying so.

Key Formulas Used in the Class 11 Maths Conic Sections Exemplar

Conic Sections is a formula-heavy chapter, and the Exemplar assumes every one of these is known before Q1. Students should be able to write this table from memory before starting the exercise.

Tip: the single most useful habit in this chapter is normalising an equation so that its right side is 1 before reading off a² and b². Q39 and Q59 both punish students who skip that step, because the tangent formula xx₁/A + yy₁/B = 1 is simply false when the right side is not 1.

Common Mistakes Students Make in the Conic Sections Exemplar

The same reflexes cost marks in this chapter every year. These five are the ones the solutions flag most often.

• Choosing a² as the bigger number in a hyperbola. That rule belongs to the ellipse. For a hyperbola, a² sits under the positive term, so in y²/4 − x²/9 = 1 it is 4, not 9. The check that e > 1 catches the slip instantly.
• Squaring the wrong variable in a parabola. When the vertex and focus share an x-coordinate the axis is vertical, so x is squared. The variable along the axis is the one that is not squared.
• Reporting the gap between two parallel tangents as the radius. That gap is the diameter, so it must be halved. Q5 is built on exactly this.
• Doubling the radius when the area doubles. Since A = πr², doubling the area multiplies r by √2 only. Writing r = 2√30 in Q10 gives a circle with four times the area.
• Reading a off the directrix constant. In Q53 the directrix is x + 5 = 0 and the vertex is (−3, 0), so a is the gap, |−3 − (−5)| = 2, not 5. One option is built precisely for students who read 5 as the distance.

How the Conic Sections Exemplar Steps Up from the NCERT Textbook

The Exemplar adds no new topics to Conic Sections. It asks the same ideas in a harder direction, as the table shows.

How to Use the Conic Sections Exemplar for Boards and JEE Preparation

This is the longest exercise in the Class 11 Maths Exemplar after Limits and Derivatives, so treat it as five sittings, not one. Finish the NCERT textbook exercises first, because the Exemplar assumes students already know the four standard parabola forms cold.

That is about 9.5 hours for the chapter. For JEE Main and JEE Advanced, the Multiple Choice block and the tangency conditions carry the most weight, and Conic Sections is a scoring chapter there every year. For CBSE Boards and CUET, the Short Answer circles and the standard ellipse and hyperbola results are the better use of time.

Practice Questions for Class 11 Maths Conic Sections

After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Conic Sections.

Other Resources for Class 11 Maths Conic Sections

Pair the Exemplar Solutions with the textbook solutions and the notes for full chapter revision. All the Conic Sections resources are linked below.

NCERT Exemplar Solutions for Other Class 11 Maths Chapters

The full Class 11 Maths Exemplar set covers 14 chapters, 735 questions and 2,625 pages of solutions. Use the table to jump to any other chapter.