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Conic Sections

Conic sections are shapes derived from slicing a double-napped cone. Learn about circles, ellipses, parabolas, and hyperbolas formed when lines intersect at various angles. Explore ellipse properties like foci, axes, vertices, and equations. Discover how eccentricity measures ellipse ovalness.

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Conic Sections

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  1. Conic Sections The geometric shapes obtained by slicing a double-napped cone A cone is formed when two lines meet at an acute angle and one of the lines is rotated around the other

  2. Circle

  3. Ellipse

  4. Parabola

  5. Hyperbola

  6. Ellipse The set of all points (x,y) the sum of whose distances from two distinct fixed points(foci) is constant

  7. MINOR AXIS CENTER (h,k) MAJOR AXIS Vertex

  8. Standard Equation of an Ellipse (x-h)^2 + (y-k)^2 a^2 b^2 = 1 (h,k) is the center of the circle a is ½ of the major axis b is ½ of the minor axis

  9. Eccentricity Measures the ovalness of an ellipse e = c/a • If c/a is small the ellipse is circular • If c/a is close to 1 then the ellipse is elongated c^2 = a^2 – b^2

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