Conic Sections and Their Equations from "summary" of NCERT Class 10 Mathematics Solutions by JagranJosh
Conic sections are the curves which are obtained by intersecting a cone with a plane. These curves include circles, ellipses, parabolas, and hyperbolas. Each of these curves has a unique geometrical shape and can be represented by a specific equation. The equations of these conic sections can be derived using the coordinates of points on the curve and certain properties of the curve. The equation of a circle is represented as (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the center of the circle and r is the radius. The equation of an ellipse is represented as x²/a² + y²/b² = 1, where a and b are the semi-major and semi-minor axes of the ellipse. The equation of a parabola is represented as y² = 4ax or x² = 4ay, where a is a constant and the vertex of the parabola is at the origin. The equation of a hyperbola is represented as x²/a² - y²/b² = 1 or y²/b² - x²/a² = 1, where a and b are constants and the ...
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