Answer
a)
A parabola 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 a focus) are equal.
b)
$x^{2} = 4py$, $y^{2} = 4px$.
Work Step by Step
a)
A parabola 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 a focus) are equal. In other words, a parabola is the set of all points that are equidistant from the directrix and the focus.
b)
The equation of a parabola with focus $(0,p)$ and directrix $y= -p$ is: $x^{2} = 4py$; if the focus is $(p,0)$, then the equation will be: $y^{2} = 4px$.
