Conic section ppt

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Conic section ppt

  1. 1. MATH-002Dr. Farhana ShaheenCONIC SECTION
  2. 2. CONIC SECTION In mathematics, a conic section (or just conic) is a curve obtained by intersecting a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2. It can be defined as the locus of points whose distances are in a fixed ratio to some point, called a focus, and some line, called a directrix.
  3. 3. CONICS The three conic sections that are created when a double cone is intersected with a plane. 1) Parabola 2) Circle and ellipse 3) Hyperbola
  4. 4. CIRCLES A circle is a simple shape of Euclidean geometry consisting of the set of points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius.
  5. 5. PARABOLA
  6. 6. PARABOLA: LOCUS OF ALL POINTS WHOSEDISTANCE FROM A FIXED POINT IS EQUAL TOTHE DISTANCE FROM A FIXED LINE. THE FIXEDPOINT IS CALLED FOCUS AND THE FIXED LINE ISCALLED A DIRECTRIX.P(x,y)
  7. 7. 2EQUATION OF PARABOLA y 4 px Axis of Parabola: x-axis Vertex: V(0,0) Focus: F(p,0) Directrix: x=-p
  8. 8. 2DRAW THE PARABOLA y 6x 2 y 4 px
  9. 9. PARABOLAS WITH DIFFERENT VALUES OF P
  10. 10. EQUATION OF THE GIVEN PARABOLA?
  11. 11. PARABOLAS IN NATURE
  12. 12. PARABOLAS IN LIFE
  13. 13. ELLIPSE: LOCUS OF ALL POINTS WHOSE SUM OFDISTANCE FROM TWO FIXED POINTS ISCONSTANT. THE TWO FIXED POINTS ARE CALLEDFOCI.
  14. 14. ELLIPSE a>b Major axis: Minor axis: Foci: Vertices: Center: Length of major axis: Length of minor axis: Relation between a, b, c
  15. 15. EQUATION OF THE GIVEN ELLIPSE?
  16. 16. EQUATION OF THE GIVEN ELLIPSE IS
  17. 17. EARTH MOVES AROUND THE SUN ELLIPTICALLY
  18. 18. DRAW THE ELLIPSE WITH CENTER AT(H,K)
  19. 19. ECCENTRICITY
  20. 20. ECCENTRICITY IN CONIC SECTIONS Conic sections are exactly those curves that, for a point F, a line L not containing F and a non- negative number e, are the locus of points whose distance to F equals e times their distance to L. F is called the focus, L the directrix, and e the eccentricity.
  21. 21. CIRCLE AS ELLIPSE A circle is a special ellipse in which the two foci are coincident and the eccentricity is 0. Circles are conic sections attained when a right circular cone is intersected by a plane perpendicular to the axis of the cone.
  22. 22. HYPERBOLA
  23. 23. HYPERBOLA Transverse axis: Conjugate axis: Foci: Vertices: Center: Relation between a, b, c
  24. 24. HYPERBOLA WITH VERTICAL TRANSVERSE AXIS
  25. 25. ECCENTRICITY E = C/A e = c/a e= 1 Parabola e=0 Circle e>1 Hyperbola e<1 Ellipse
  26. 26. ECCENTRICITY EELLIPSE (E=1/2), PARABOLA (E=1) ANDHYPERBOLA (E=2) WITH FIXED FOCUS F ANDDIRECTRIX
  27. 27. HYPERBOLA
  28. 28. THANK YOU

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