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Mathematics Project

Mathematics Project. Done by : HAMAD SALEM ALRAWAHI AHMAD ABDULLA ALBAK HAMAD FAHEM ALHEBSI ADBULLAH AHMED 12-06 To : Nihad Al Abdallah. Our project about :. Introduction. First what is the conic section ?

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Mathematics Project

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  1. Mathematics Project Done by : HAMAD SALEM ALRAWAHI AHMAD ABDULLA ALBAK HAMAD FAHEM ALHEBSI ADBULLAH AHMED 12-06 To :Nihad Al Abdallah

  2. Our project about :

  3. Introduction First what is the conic section ? AConic Section is a curve that is obtained by the intersection of a cone with a plane. Each conic section has points called focus and directrix. There are four main conic sections, which are: Circle, Ellipse, Parabola and hyperbola.

  4. Circle The circle is a simple closed curve and its set of points is in a plane that has a given distance from a given point that is called the center. The distance between any of the points and the center is called the radius. The circle is mostly used for geometry and astronomy and calculus in mathematics.

  5. Ellipse The ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant. Ellipses are mainly used in astronomy applications.

  6. Parabola The parabolais created from the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface and it makes out an open curve. Parabolas shaped mirrors are used in most modern reflecting telescopes and in satellite dishes and radar receivers.

  7. Hyperbola The Hyperbolais a type of smooth curve, lying in a plane that are the same distances from a given point called focus and a given line called directrix and it makes an open curve. Hyperbola is used in many places mainly to construct bridges.

  8. Comprehensive comparison between conics

  9. Comprehensive comparison between conics

  10. Comprehensive comparison between conics

  11. Comprehensive comparison between conics

  12. Parabola 𝑦 = a𝑥2 + b𝑥 + c Since it passes through (0,3) 3= a(0)2 + b(0) + c c = 3 𝑦 = a𝑥2 + b𝑥 + 3 -Addition 2a – b + a + b = 2 + 1 3a = 3 a = 1 a + b = 1 1 + b = 1 b = 0 Equation: 𝑦 = a𝑥2 + b𝑥 + c 𝑦 = 1𝑥2 + 0(𝑥) + 3 𝑦 = x2 + 3 Since it passes through (-2,7) 7 = a(-2)2 + b(-2) + 3 7 = 4a – 2b + 3 4 = 4a – 2b ( 4a – 2b = 4 )/2 2a – b = 2 Passes Through (1,4) 4 = a(1)2 + b(1) + 3 1 = a + b

  13. Circle 𝑥 + 2𝑦 = 2 𝑥 = 2 - 2𝑦 𝑥2 + 𝑦2 = 25 (2 - 2𝑦)2 + 𝑦2 = 25 (2 - 2𝑦) (2 - 2𝑦) + 𝑦2 = 25 4 - 4𝑦 - 4𝑦 + 4𝑦2 + 𝑦2 = 25 5𝑦2 - 8𝑦 - 21 = 0 𝑦 = 3 𝑦 = -1.4 • 𝑥 = 2 – 2(3) or 𝑥 = 2 – 2(-1.4) • 𝑥 = 4 𝑥 = 4.8 • Two Points: • (-4,3) • (4.8,-1.4)

  14. Circle Circle: 𝑥2 + 𝑦2 = 25 Line: 𝑥 + 2𝑦 = 2 Center(0,0), Radius: 5

  15. Physics 𝑦 = a(𝑥 - h) + k, a<0 Since focus is at origin h=0 Vertex (h,k) = (0,20) Equation of the parabolic path:

  16. Halley’s Comet The distance between the sun and earth is 146 million km.

  17. Halley’s Comet Equation of hyperbola:

  18. Pictures

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