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Conic Sections

Telangana Open School (TOSS) · Class 12 · Mathematics

Complete topic list for Conic Sections in Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

57 questions22 flashcards5 concepts

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4 Topics · Telangana Open School (TOSS) Class 12 Mathematics

Topics in Conic Sections

1

Basic Concepts of Conic Sections

  • A conic section is the locus of a point that moves such that its distance from a fixed point (focus) is in a constant ratio to its perpendicular distance from a fixed line (directrix).
  • This constant ratio is called eccentricity (e).
  • The type of conic depends on the value of e: if e < 1 → ellipse, e = 1 → parabola, e > 1 → hyperbola.
2

Ellipse

  • An ellipse is the locus of a point where the sum of distances from two fixed points (foci) is constant, or equivalently, where the ratio of distance from focus to directrix is less than 1 (e < 1).
  • Standard equation: \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) where a > b.
  • Major axis = 2a, Minor axis = 2b.
3

Parabola

  • A parabola is the locus of a point equidistant from a fixed point (focus) and a fixed line (directrix).
  • Standard equation: \(y^2 = 4ax\) — opens right, vertex at origin.
  • Other forms: \(y^2 = -4ax\) (left), \(x^2 = 4ay\) (up), \(x^2 = -4ay\) (down).
4

Tangents, Normals, and Pole-Polar

  • Condition for line y = mx + c to be tangent to ellipse: c² = a²m² + b².
  • Equation of tangent to ellipse at (x₁,y₁): \(\frac{xx_1}{a^2} + \frac{yy_1}{b^2} = 1\).
  • Equation of normal: \(\frac{a^2x}{x_1} - \frac{b^2y}{y_1} = a^2 - b^2\).

Key Concepts

Central concept: Conic Sections

Definition of Conic SectionTypes of ConicsParabolaEllipseKey ElementsTangents and NormalsPole and Polar

Frequently Asked Questions

What are the important topics in Conic Sections for Telangana Open School (TOSS) Class 12 Mathematics?
Conic Sections covers several key topics that are frequently asked in Telangana Open School (TOSS) Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Conic Sections — Telangana Open School (TOSS) Class 12 Mathematics?
Understand the core concepts first, then work through the 57 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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