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Summary

  • The set of all points in a plane which are equidistant from a fixed point is a plane.
  • The equation of a circle with the radius "r" and centre (h, k) is (x - h)2 + (y - k)2 = r2
  • A conic section is the locus of a point which moves such that its distance from a fixed point always bears a constant ratio to its distance from a fixed line all being in the same plane.
  • Depending on the eccentricity e, the conics are classified as follows
    1. if e = 0, the conic formed is a circle;
    2. if e < 1, the conic formed is an ellipse;
    3. if e = 1, the conic formed is a parabola;
    4. if e > 1, the conic formed is a hyperbola.
  • A parabola is the locus of a point which moves in a plane such that its distance from a fixed point in the plane is always a constant equal to its distance from a fixed straight line in the same plane.
  • The equation of a parabola with focus (a, 0) where a > 0 and directrix x = -a is y2 = 4ax.
  • The latus rectum of a parabola is a chord passing through the focus and perpendicular to the axis. The length of the latus rectum of a parabola y2 = 4ax is 4a.
  • An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant.
  • The equation of an ellipse with foci on the x - axis is .
  • The latus rectum of an ellipse is a chord passing through any of the foci and perpendicular to the major axis. The length of the latus rectum of an ellipse is .
  • The hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant.
  • The equation of a hyperbola with foci on the x - axis is : .
  • Latus rectum of a hyperbola is a chord passing through any of the foci and perpendicular to the transverse axis. Its length is .




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