Question

What is the equation of the parabola with a focus at (0,0) and a directrix of y= -3?

Answer 1

The equation of the parabola is `y=1/6*x^2-1.5`

Explanation:

Vertex is at mid point between focus`(0,0)`and directrix `(y=-3)`So vertex is at `(0,-1.5)` The equation of parabola is`y=a(x-0)^2-1.5=ax^2-1.5` Distance(d) of vertex from directrix is 1.5 and we know `d=1/(4|a|) or a = 1/(4*1.5)=1/6`Hence the equation of the parabola is `y=1/6*x^2-1.5` graph{1/6*x^2-1.5 [-10, 10, -5, 5]}