Question

Find the equation of the set of points which are equidistant from the origin and the line x = −2. Sketch this set of points.

Answer 1

Answer:   y² = 8x    

Step-by-step explanation:

The set of points which are equidistant from one point and from a line is a parabola.

In this particular case we have directrix line × = -2 so that means focus must be on the x-axis and with coordenates f (2,0) and p = 2 (the distance between the vertex and the focus with that information we can get the equation

vertex ( 0, 0)     p = 2 the parabola open to the left so is of the form

y² =- 4*p*×           ⇒  y² = 8x