Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-3, 3] by [-3, 3]. Directrix y = -1, e = 3

Question

Quizplus · Accepted Answer

The given directrix is a horizontal line at y=-1, which means the axis of the parabola is vertical. Since the focus is at (0,0), the vertex must also be at (0,0).

Using the formula for eccentricity, e=distance between focus and directrix / distance between vertex and directrix, we can solve for a.

e = 3 , distance between focus and directrix = 1 (since it's a horizontal line and the focus is (0,0)), so 
a = (1/3) distance between vertex and directrix.

Since the directrix is y=-1, we can see that the distance between the vertex and directrix is also 1. Therefore, a = 1/3.

Since the axis is vertical and the vertex is at the origin, the equation of the parabola is of the form x^2 = 4ay. Plugging in a=1/3, we get x^2 = (4/3)y.

Using a graphing utility and the given window size of [-3,3] by [-3,3], we can see that the graph matches Option C.

Use a Graphing Utility to Graph the Conic Section with Focus