Answer
(a) A parabola is the set of all points that are equidistant from the directrix and the focus. Also, it is the set of all points in a plane such that the distance from a line called the directrix and the distance from a fixed point called focus are equal.
(b) Equation of a parabola with focus $(0,p)$ and directrix
$y= -p$ is:
$$x^{2} = 4py$$
When the focus is $(p,0)$, then the equation will be:
$$y^{2} = 4px$$
Work Step by Step
(a) A parabola is the set of all points that are equidistant from the directrix and the focus. Also,it is the set of all points in a plane such that the distance from a line called the directrix and the distance from a fixed point called focus are equal.
(b) Equation of a parabola with focus $(0,p)$ and directrix
$y= -p$ is:
$$x^{2} = 4py$$
When the focus is $(p,0)$, then the equation will be:
$$y^{2} = 4px$$
