Question

Find an equation for the parabola that has its vertex at the origin

and has its focus at the point: (0,-7.9)

Answer 1

y = 0.0633 x^2

Explanation:

Since the vertex of the parabola is at the origin, the equation of the parabola can be written in the form:

y = a x^2

where a is a constant that determines the shape of the parabola.

The focus of the parabola is at the point (0,-7.9). Recall that the focus of a parabola is a point that is equidistant from the vertex and the directrix. Since the vertex is at the origin, the directrix must be a horizontal line that is 7.9 units above the vertex. Therefore, the equation of the directrix is:

y = 7.9

The distance between the vertex and the focus is equal to the distance between the vertex and the directrix. This distance is given by:

d = |-7.9 - 0|/2 = 3.95

Therefore, the constant a can be found by solving the equation:

a = 1/(4d) = 1/(4(3.95)) = 0.0633

So the equation of the parabola is:

y = 0.0633 x^2