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Conic Sections — Revision Notes

Telangana Open School (TOSS) · Class 12 · Mathematics

Conic Sections revision notes for Telangana Open School (TOSS) Class 12 Mathematics: 4 topics in quick points.

57 questions22 flashcards22 formulas & key relations5 concepts

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Key Topics to Revise

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: \(\frac{a^2x}{x_1} - \frac{b^2y}{y_1} = a^2 - b^2\).

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Full Notes

Key Concepts

A conic section is the pathA parabola is the setAn ellipse is the locusThe tangent to a conic atIf two tangents are drawn from

Frequently Asked Questions

What are the important topics in Conic Sections for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Conic Sections include Basic Concepts of Conic Sections, Ellipse, Parabola, Tangents, Normals, and Pole-Polar. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Conic Sections for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 57 practice questions on Conic Sections. Revise 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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All Telangana Open School (TOSS) Class 12 Mathematics Revision Notes

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