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line at infinity sentence in Hindi

"line at infinity" meaning in Hindiline at infinity in a sentence
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  • In a pappian projective plane ( one defined over a field ), all conic sections are equivalent to each other, and the different types of conic sections are determined by how they intersect the line at infinity, denoted by ?.
  • The pencil of circles of equations a ( x ^ 2 + y ^ 2-1 )-bx = 0 degenerates for a = 0 into two lines, the line at infinity and the line of equation x = 0.
  • In order to turn this process into a correlation, the Euclidean plane ( which is not a projective plane ) needs to be expanded to the extended euclidean plane by adding a line at infinity and points at infinity which lie on this line.
  • When extending the concept of line to the line at infinity, a set of "'parallel planes "'can be seen as a " sheaf of planes " intersecting in a " line at infinity ".
  • When extending the concept of line to the line at infinity, a set of "'parallel planes "'can be seen as a " sheaf of planes " intersecting in a " line at infinity ".
  • There are advantages in being able to think of a hyperbola and an ellipse as distinguished only by the way the hyperbola " lies across the line at infinity "; and that a parabola is distinguished only by being tangent to the same line.
  • Geometrically, the line at infinity is not special, so while some conics intersect the line at infinity differently, this can be changed by a projective transformation  pulling an ellipse out to infinity or pushing a parabola off infinity to an ellipse or a hyperbola.
  • Geometrically, the line at infinity is not special, so while some conics intersect the line at infinity differently, this can be changed by a projective transformation  pulling an ellipse out to infinity or pushing a parabola off infinity to an ellipse or a hyperbola.
  • If two pairs of opposite sides are parallel, then all three pairs of opposite sides form pairs of parallel lines and there is no Pascal line in the Euclidean plane ( in this case, the line at infinity of the extended Euclidean plane is the Pascal line of the hexagon ).
  • If the conic is non-degenerate, the conjugates of a point always form a line and the polarity defined by the conic is a bijection between the points and lines of the extended plane containing the conic ( that is, the plane together with the points and line at infinity ).
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