Conic Sections Circle Parabola Hyperbola Ellipse x2/a2-y2/b2=1 Application of Hyperbolas in Real Life : * Lampshade. A household lamp casts hyperbolic shadows on a wall. * Cooling Towers of Nuclear Reactors The hyperboloid is the design standard for all nuclear cooling towers. Definition A parabola is the set of all points such that the distance between a point on the parabola and a fixed line is the same as the distance between a point on the parabola and a fixed point Definition: A hyperbola is the set of all points P in a plane such that absolute value of the difference of the distances from P to two fixed points F1 and F2 is constant. Equation (x - h)^2 = 4p(y - k) (y - k)^2 = 4p(x - h) Application of Parabolas Antenna: All incoming rays parallel to the axis of the parabola are reflected through the focus Car headlites to reflect the light rays emanating from the focus of the parabola The cables of a well-designed suspension bridge follow a parabolic curve. A circle is all points equidistant, (This distance is called the radius), from one point (the center of the circle). A circle can be formed by slicing a right circular cone with a plane traveling parallel to the base of the cone. Origin (h , k)

(x-h)2 + (y-k)2 = r2

Origin (0 , 0)

X2 + Y2 = r2 Definition : Equation : Applications of Circles : During the full moon phase, it appears as a circle in the sky. gears are a good example of the circle conic. The gears intersect in order to keep spinning. A curved line forming a closed loop, where the sum of the distances from two points (foci) to every point on the line is constant. Definition : Equation : (x - h)2 / a2 + (y - k)2 / b2 = 1 Application : The orbits of the planets are ellipses, not circles. This was first discovered by Johannes Kepler based on his careful observations Medical specialists used the ellipse to invent a device that effectively treats kidney stones and gallstones. shockwaves are used to successfully shatter a painful kidney stone (or gallstone) into tiny pieces that can be easily passed by the body. This medical application is called lithotripsy.

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# Math Presentation - Conic Sections

Circle
Parabola
Hyperbola
Ellipse

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