Maths · Class 11 · Co-ordinate Geometry

Conic Sections (Parabola, Ellipse, Hyperbola) for JEE

Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.

Last updated: 26 October 2026

Direct answer

Standard equations, focus, directrix, eccentricity, latus rectum, parametric forms, tangents and normals of parabola, ellipse and hyperbola.

Key ideas

Conic Sections (Parabola, Ellipse, Hyperbola): what you must understand

Eccentricity: parabola e = 1, ellipse e < 1, hyperbola e > 1
Focal distance property of ellipse: PS + PS′ = 2a
Parametric points simplify tangent and normal questions
Condition for tangency: c² = a²m² ± b²

Formula sheet

Must-know formulas for Conic Sections (Parabola, Ellipse, Hyperbola)

Parabola y² = 4ax: focus (a, 0), LR = 4a, tangent y = mx + a/m
Ellipse: b² = a²(1 − e²), LR = 2b²/a
Hyperbola: b² = a²(e² − 1)
Ellipse tangent condition: c² = a²m² + b²

One-page formula sheet

Printable Conic Sections (Parabola, Ellipse, Hyperbola) formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

Avoid

Common mistakes students make

Mixing ellipse and hyperbola b² relations
Wrong focus for vertical conics
Forgetting both tangents in slope form

For the exam

How this topic is asked in JEE

Appears in almost every JEE Main shift. Very high frequency in JEE Main. Parabola questions are the most common.

Prerequisites: Circles.

NCERT map

Where Conic Sections (Parabola, Ellipse, Hyperbola) is in NCERT

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Class	Book	Chapter	Sections JEE asks from
Class 11	Mathematics	Conic Sections	Parabola; Ellipse; Hyperbola; Standard equations of parabola; Standard equations of an ellipse; Standard equations of hyperbola; Latus rectum

JEE Advanced level

A JEE Advanced-level example on Conic Sections (Parabola, Ellipse, Hyperbola)

Question. A tangent to the parabola y² = 8x makes an angle of 45° with the positive x-axis. Find the equation of this tangent, the point of contact on the parabola, and the area of the triangle formed by this tangent, the x-axis, and the latus rectum of the parabola.

Show solution

For y² = 8x, we get 4a = 8, so a = 2. The tangent with slope m to y² = 4ax is y = mx + a/m. With m = tan(45°) = 1, the tangent is y = x + 2.
Point of contact for tangent y = mx + a/m is (a/m², 2a/m). Substituting a = 2 and m = 1 gives point of contact as (2, 4).
Tangent y = x + 2 meets the x-axis (y = 0) at point A = (−2, 0).
The latus rectum is the line x = 2. It meets the x-axis at B = (2, 0) and meets the tangent at C = (2, 4).
Triangle ABC has vertices (−2, 0), (2, 0), and (2, 4). Base AB = 4 units along x-axis, height = 4 units. Area = (1/2) × 4 × 4 = 8 square units.

Answer: Tangent: y = x + 2, Point of contact: (2, 4), Area of triangle: 8 square units

This example was solved twice independently and both solutions agree.

Free lectures

Best free lectures for Conic Sections (Parabola, Ellipse, Hyperbola)

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

CONIC SECTIONS in 70 minutes || Complete Chapter for JEE Main/Advanced — JEE Wallah, 1:12:46
Conics One Shot | JEE Main 2024 | RRR — JEE Nexus by Unacademy, 2:30:50
Jump to a subtopic (11)
- 0:00 Introduction
- 4:08 General equation of Conic & Identification
- 11:10 Standard Parabolas
- 41:16 Standard Ellipses
- 1:14:07 Standard Hyperbola
- 1:33:33 Conjugate and Rectangular Hyperbola
- 1:37:49 Parametric form of a Conic
- 1:47:53 Position of a point w.r.t. a conic
- 1:48:23 Focal Chord and Focal distances in Conics
- 2:07:04 Chords of a conic
- 2:18:30 Properties of Conics

Practise

Where to practise for free

25 JEE Main 2026 PYQs on Conic Sections (Parabola, Ellipse, Hyperbola), with solutions.
Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
See it move: interactive simulation.

FAQs

Frequently asked questions

Is Conic Sections (Parabola, Ellipse, Hyperbola) important for JEE Main 2027?

Appears in almost every JEE Main shift. It is part of the official 'Co-ordinate Geometry' unit in the JEE Main 2027 syllabus.

What are the most important formulas in Conic Sections (Parabola, Ellipse, Hyperbola)?

Parabola y² = 4ax: focus (a, 0), LR = 4a, tangent y = mx + a/m; Ellipse: b² = a²(1 − e²), LR = 2b²/a; Hyperbola: b² = a²(e² − 1).

How should I study Conic Sections (Parabola, Ellipse, Hyperbola) for JEE?

Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. Very high frequency in JEE Main. Parabola questions are the most common.