Question

practice using the focus and directrix to define a parabola. when the focus and directrix are used to derive the equation of a parabola, two distances were set equal to each other. $sqrt{(x - x)^2+(y - (-p))^2}=sqrt{(x - 0)^2+(y - p)^2}$ the distance between the directrix and is set equal to the distance and the same point on the a point on the parabola x the axis of symmetry the focus the origin

Explanation:

Step1: Recall parabola definition

A parabola is defined as the set of all points that are equidistant from a fixed - point (the focus) and a fixed - line (the directrix).

Step2: Identify distances in formula

In the formula $\sqrt{(x - x)^2+(y - (-p))^2}=\sqrt{(x - 0)^2+(y - p)^2}$, the left - hand side represents the distance between a point $P(x,y)$ on the parabola and the point $Q(x, - p)$ on the directrix $y=-p$, and the right - hand side represents the distance between the point $P(x,y)$ on the parabola and the focus $F(0,p)$.

Answer:

the focus