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Slope, forms of a line, angle between lines, distance formulas, family of lines and locus problems.
Maths · Class 11 · Co-ordinate Geometry
Straight Lines 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
Key ideas
Straight Lines: what you must understand
- Parallel lines have equal slopes; perpendicular slopes multiply to −1
- Family of lines through intersection: L₁ + λL₂ = 0
- Distance of a point from a line
- Centroid, incentre, orthocentre basics
Formula sheet
Must-know formulas for Straight Lines
- Slope m = (y₂ − y₁)/(x₂ − x₁)
- Distance from (x₁, y₁) to ax + by + c = 0: |ax₁ + by₁ + c|/√(a² + b²)
- tanθ = |(m₁ − m₂)/(1 + m₁m₂)|
- Distance between parallel lines: |c₁ − c₂|/√(a² + b²)
Print
One-page formula sheet
Printable Straight Lines formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.
Avoid
Common mistakes students make
- Ignoring vertical lines (undefined slope)
- Sign errors in distance formula
- Missing the second angle bisector
For the exam
How this topic is asked in JEE
Appears frequently. Base for all coordinate geometry. Speed here helps conics.
NCERT map
Where Straight Lines 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 | Straight Lines | Slope of a Line; Various Forms of the Equation of a Line; General Equation of a Line; Distance of a Point From a Line |
JEE Advanced level
A JEE Advanced-level example on Straight Lines
Question. A variable line L passes through the fixed point P(2, 3) and intersects the x-axis at A and y-axis at B. Find the equation of the locus of the centroid of triangle OAB, where O is the origin.
Show solution
- Let line L have x-intercept a and y-intercept b, so A = (a, 0) and B = (0, b). Line equation: x/a + y/b = 1
- Since P(2, 3) lies on L: 2/a + 3/b = 1
- Centroid G of triangle OAB with O(0,0), A(a,0), B(0,b) is G = (a/3, b/3)
- Let G = (h, k), so a = 3h and b = 3k. Substitute into the condition from step 2: 2/(3h) + 3/(3k) = 1
- Simplify: 2k + 3h = 3hk. Replace h → x and k → y to get the locus
Answer: 3x + 2y = 3xy (or equivalently 2/x + 3/y = 3)
This example was solved twice independently and both solutions agree.
Free lectures
Best free lectures for Straight Lines
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.
- Straight Lines FULL CHAPTER | Class 11th Maths | Arjuna JEE — Arjuna JEE, 5:08:31
Jump to a subtopic (17)
- 00:00 Introduction
- 31:12 4 Center of a Triangle
- 56:58 Locus
- 01:22:05 3 Important Terms of a Straight Line
- 01:30:31 Horizontal & Vertical Line
- 01:36:08 Various Forms of a Straight Line
- 01:59:52 Angle Between Lines
- 02:34:45 Perpendicular Distance of a Point From A Line
- 02:50:40 Family of Lines
- 03:08:41 Parametric Form of a Straight Line
- 03:35:57 Formula - Foot of perpendicular & Image of a Point
- 03:49:21 General 2' Equation
- 04:01:29 Angle Between Pair of Lines
- 04:06:32 Homogenous 2' Equation
- 04:13:25 Equation of Angle Bisectors
- 04:21:04 PYQs
- 05:07:49 Thank You Bachoo!!
- STRAIGHT LINES in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 7:44:47
Jump to a subtopic (27)
- 00:00 Introduction
- 01:18 Topics to be covered
- 02:50 Section Formula
- 07:55 Area of Triangle
- 14:15 Collinear Points
- 20:40 Slope of Line
- 31:24 Equation of Line
- 1:24:15 Angle Between Lines
- 1:58:44 Information about Triangle
- 2:30:12 Four centers of Triangle
- 2:32:24 Formula for Circumradius & Inradius
- 2:40:40 Important Theorems
- 3:55:08 Important Results
- 4:13:12 Perpendicular distance of a point from a line
- 4:29:35 Distance between two parallel lines
- 4:31:07 Area of parallelogram
- 4:45:06 Image & foot of perpendicular
- 4:52:37 Optics problem
- 5:28:12 Congruency of lines
- 5:30:06 Angle bisector
- 5:34:05 Isolating acute/obtuse angle bisector
- 5:39:15 Angle bisect containing point
- 5:57:55 Shifting of origin & rotation of axis
- 6:07:00 Family of straight lines
- 6:15:44 Pair of straight line
- 7:17:43 Locus problems
- 7:44:20 Thank you bachhon
Practise
Where to practise for free
- 9 JEE Main 2026 PYQs on Straight Lines, 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 Straight Lines important for JEE Main 2027?
Appears frequently. It is part of the official 'Co-ordinate Geometry' unit in the JEE Main 2027 syllabus.
What are the most important formulas in Straight Lines?
Slope m = (y₂ − y₁)/(x₂ − x₁); Distance from (x₁, y₁) to ax + by + c = 0: |ax₁ + by₁ + c|/√(a² + b²); tanθ = |(m₁ − m₂)/(1 + m₁m₂)|.
How should I study Straight Lines 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. Base for all coordinate geometry. Speed here helps conics.