11th Mathematics NCERT Chapter 10
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– Introduction to Conic Sections: Study of circles, ellipses, parabolas, and hyperbolas derived from intersections of a plane with a double napped right circular cone. These curves have applications in various fields like planetary motion and optic designs.
– Circle, Ellipse, Parabola, and Hyperbola: Details on how different types of conic sections (circle, ellipse, parabola, hyperbola) are formed based on the intersection of a plane with a cone at varying angles. Includes equations and properties specific to each curve【4:0†source】【4:1†source】.
– Historical Significance: A brief historical note on the development of geometry, specifically focusing on the works of ancient Greek geometers like Euclid and Apollonius in the study of conic sections【4:1†source】.
– Miscellaneous Exercises: Practical exercises involving conic sections, such as finding focuses, determining equations, and exploring geometric properties in different scenarios like parabolic reflectors, suspension bridges, and inscribed triangles【4:3†source】.
What is the equation of the ellipse with vertices at (±13, 0) and foci at (±5, 0)?
The equation of the ellipse is 25x^2/169 + y^2/144 = 1
Find the equation of the hyperbola where the foci are (0, ±3) and the vertices are (0, ±11/2).
The equation of the hyperbola is 100y^2/121 – 44x^2/25 = 1
Determine the equation of the ellipse with a major axis length of 20 and foci at (0, ±5).
The equation of the ellipse is 75x^2/100 + y^2/75 = 1
What is the equation of the ellipse passing through the points (4, 3) and (–1, 4)?
The equation of the ellipse is 7x^2/247 + 15y^2/247 = 1
Find the equation of the hyperbola with foci at (0, ±12) and a latus rectum length of 36.
The equation of the hyperbola is 3y^2 – x^2 = 108
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