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Conic section

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Mxolisi Creswell MNCUBE
Mxolisi Creswell MNCUBE

This document discusses conic sections, which are curves formed by the intersection of a cone with a plane. The three types of conic sections are circles, ellipses, and hyperbolas. Parabolas are also conic sections. Circles are defined as all points equidistant from a center point. Ellipses are defined as all points whose sum of distances to two focal points is a constant. Hyperbolas are defined as two branches where the difference between the distances to two focal points is a constant. The eccentricity parameter relates the conic section's shape to the distance between its foci and directrix.

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CONIC SECTION MATH-002 Dr. Farhana Shaheen
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.
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
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.
PARABOLA
PARABOLA: LOCUS OF ALL POINTS WHOSE DISTANCE FROM A FIXED POINT IS EQUAL TO THE DISTANCE FROM A FIXED LINE. THE FIXED POINT IS CALLED FOCUS AND THE FIXED LINE IS CALLED A DIRECTRIX. P(x,y)
EQUATION OF PARABOLA Axis of Parabola: x-axis Vertex: V(0,0) Focus: F(p,0) Directrix: x=-p pxy 42
DRAW THE PARABOLA xy 62 pxy 42
PARABOLAS WITH DIFFERENT VALUES OF P
EQUATION OF THE GIVEN PARABOLA?
PARABOLAS IN NATURE
PARABOLAS IN LIFE
ELLIPSE: LOCUS OF ALL POINTS WHOSE SUM OF DISTANCE FROM TWO FIXED POINTS IS CONSTANT. THE TWO FIXED POINTS ARE CALLED FOCI.
ELLIPSE a > b Major axis: Minor axis: Foci: Vertices: Center: Length of major axis: Length of minor axis: Relation between a, b, c
Conic section
EQUATION OF THE GIVEN ELLIPSE?
EQUATION OF THE GIVEN ELLIPSE IS
EARTH MOVES AROUND THE SUN ELLIPTICALLY
DRAW THE ELLIPSE WITH CENTER AT(H,K)
ECCENTRICITY
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.
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.
HYPERBOLA
HYPERBOLA Transverse axis: Conjugate axis: Foci: Vertices: Center: Relation between a, b, c
HYPERBOLA WITH VERTICAL TRANSVERSE AXIS
ECCENTRICITY E = C/A e = c/a e= 1 Parabola e=0 Circle e>1 Hyperbola e<1 Ellipse
ECCENTRICITY E ELLIPSE (E=1/2), PARABOLA (E=1) AND HYPERBOLA (E=2) WITH FIXED FOCUS F AND DIRECTRIX
HYPERBOLA
Conic section
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Conic section

  • 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. 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. 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.
  • 6. PARABOLA: LOCUS OF ALL POINTS WHOSE DISTANCE FROM A FIXED POINT IS EQUAL TO THE DISTANCE FROM A FIXED LINE. THE FIXED POINT IS CALLED FOCUS AND THE FIXED LINE IS CALLED A DIRECTRIX. P(x,y)
  • 7. EQUATION OF PARABOLA Axis of Parabola: x-axis Vertex: V(0,0) Focus: F(p,0) Directrix: x=-p pxy 42
  • 8. DRAW THE PARABOLA xy 62 pxy 42
  • 10. EQUATION OF THE GIVEN PARABOLA?
  • 13. ELLIPSE: LOCUS OF ALL POINTS WHOSE SUM OF DISTANCE FROM TWO FIXED POINTS IS CONSTANT. THE TWO FIXED POINTS ARE CALLED FOCI.
  • 14. ELLIPSE a > b Major axis: Minor axis: Foci: Vertices: Center: Length of major axis: Length of minor axis: Relation between a, b, c
  • 16. EQUATION OF THE GIVEN ELLIPSE?
  • 17. EQUATION OF THE GIVEN ELLIPSE IS
  • 18. EARTH MOVES AROUND THE SUN ELLIPTICALLY
  • 19. DRAW THE ELLIPSE WITH CENTER AT(H,K)
  • 21. 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.
  • 22. 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.
  • 24. HYPERBOLA Transverse axis: Conjugate axis: Foci: Vertices: Center: Relation between a, b, c
  • 25. HYPERBOLA WITH VERTICAL TRANSVERSE AXIS
  • 26. ECCENTRICITY E = C/A e = c/a e= 1 Parabola e=0 Circle e>1 Hyperbola e<1 Ellipse
  • 27. ECCENTRICITY E ELLIPSE (E=1/2), PARABOLA (E=1) AND HYPERBOLA (E=2) WITH FIXED FOCUS F AND DIRECTRIX