Overview
RD Sharma Class 11 Mathematics Chapter 26 focuses on one of the most elegant curves in coordinate geometry — the Ellipse. It is a type of conic section obtained when a plane cuts a cone at an angle, resulting in a closed, oval-shaped figure. The ellipse generalizes the concept of a circle and introduces students to the idea of eccentricity and locus-based equations.
This chapter from RD Sharma Class 11 Maths builds upon the concept of a parabola and serves as a gateway to higher analytical geometry.
Key Concepts
An ellipse is defined as the set of all points in a plane such that the sum of their distances from two fixed points (called foci) is constant. The midpoint of the line joining the foci is the center, and the line through the foci is the major axis.
Standard Forms
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Ellipse centered at origin (horizontal major axis):
( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 ), where ( a > b ) -
Ellipse centered at origin (vertical major axis):
( \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1 ), where ( a > b ) -
Eccentricity (e): ( e = \sqrt{1 - \frac{b^2}{a^2}} )
Topics Covered
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Definition and derivation of ellipse equation
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Terms like center, focus, vertex, directrix, and eccentricity
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Equation of ellipse in different positions
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Finding coordinates of foci and vertices
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Relation between semi-major and semi-minor axes
Applications
Ellipses are found in planetary orbits, optics, and design of reflective surfaces. The real-life application of ellipse equations helps students connect abstract geometry to physical phenomena like planetary motion (Kepler’s laws).
RD Sharma Solutions
The RD Sharma textbook presents multiple examples and exercises that gradually increase in difficulty, ensuring conceptual and numerical clarity. Stepwise RD Sharma solutions guide students in mastering coordinate geometry techniques.
Conclusion
Chapter 26 builds a strong conceptual base for geometry and helps students appreciate how mathematical equations can describe real-world curved paths.