   This chapter is about    parabola, hyperbolas, circles, ellipses.   the names parabola and hyperbola are    given by ...
   When the plane cuts at the vertex of    the cone, we have the following    different cases:   When α < β ≤ 90 then th...
: (x - h)2 + (y - k)2 = r2
   Left handed parabola:   y²= 4ax. X=-a, f(a.0).   .   Right handed parabola: y²=-4ax. X=+a, f(-a,0).
   Upward parabola   Downward parabola
   Latus rectum of a parabola is a line segment    perpendicular to the axis of the parabola, through    the focus and wh...
   An ellipse is the set of all the points in a plane,    the sum of whose distances from two fixed    points in the plan...
   Major axis= 2a.   Minor axis=2f   Foci=2c. Relationship: A²=b²+c². C=√a²-b².
 The  eccentricity of an ellipse is the ratio of the distances from the centre of the ellipse to one of the foci and to o...
 Latus rectum of an ellipse is a line  segment perpendicular to the  major axis through any of the foci  and whose end po...
                                          .   Standard equations of the hyperbola:
 Latus  rectum of an hyperbola  is a line segment perpendicular  to the transverse axis through  any of the foci and whos...
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
Mehul mathematics conics
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Mehul mathematics conics

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Mehul mathematics conics

  1. 1.  This chapter is about parabola, hyperbolas, circles, ellipses. the names parabola and hyperbola are given by Apollonius. These curves are in fact, known as conic sections or more commonly conics because they can be obtained as intersections of a plane with double napped right circular cones.
  2. 2.  When the plane cuts at the vertex of the cone, we have the following different cases: When α < β ≤ 90 then the section is a point. When β = α the plane contains a generator of the cone and the section is a straight line. When 0≤ β < α the section is a pair of intersecting straight lines.
  3. 3. : (x - h)2 + (y - k)2 = r2
  4. 4.  Left handed parabola: y²= 4ax. X=-a, f(a.0). . Right handed parabola: y²=-4ax. X=+a, f(-a,0).
  5. 5.  Upward parabola Downward parabola
  6. 6.  Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose end points lie on the parabola Length of latus rectum= 4a.
  7. 7.  An ellipse is the set of all the points in a plane, the sum of whose distances from two fixed points in the plane is a constant.
  8. 8.  Major axis= 2a. Minor axis=2f Foci=2c. Relationship: A²=b²+c². C=√a²-b².
  9. 9.  The eccentricity of an ellipse is the ratio of the distances from the centre of the ellipse to one of the foci and to one of the vertices of the ellipse.It is denoted by e= c⁄a.
  10. 10.  Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose end points lie on the ellipse. Length of the latus rectum of an ellipse:
  11. 11.  . Standard equations of the hyperbola:
  12. 12.  Latus rectum of an hyperbola is a line segment perpendicular to the transverse axis through any of the foci and whose end points lie on the hyperbola. Length of latus rectum in hyperbola: 2b2/a

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