Question

what is hyperbola, parabola, locus??

Answer 1

hyperbola :- a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.
parabola :- a symmetrical open plane curve formed by intersection of a cone with plane parallel to its side. for example path of projectile under this gravity's influence.
locus :- a curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.
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Answer 2

   In cartesian coordinate system, the locus of a point P(a,b) is the description of the path that point takes based on a given condition.  The path is expressed in the form of a relation between x coordinate and y coordinate of the point P.

  The relationship between a and b is derived on the basis of a condition that is given. Then a is replaced by x and b is replaced by y. 

Hyperbola is a conic section. That means we can cut a hollow (double) cone to get this hyperbola curve containing two disconnected curves. They are symmetric.
    we cut the double cone with a plane that is not parallel to the slanting edge   of the cone. The angle of the plane to the base of the cone is more than the angle that the slanting edge makes with the base of the cone.

Hyperbola is the locus of a point P(x, y) such that the absolute value of the difference between two distances PF1 and PF2 to two fixed points F1 and F2 is a constant.  The two points are called the foci.

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Parabola is a conic section which is the result of cutting of a hollow double cone with a plane parallel to the slanting edge of the double cone.

Parabola is also defined as the locus of a point P(x,y) which is equidistant from a straight line D (called directrix) and a fixed point F (called the focus).