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 x = 2, e = 1

Question

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The conic section with focus (0, 0) and directrix x = 2 and eccentricity 1 is a parabola opening to the left. The equation of the directrix in terms of y is y = 0, so the focus is at (-e, 0) = (-1, 0). The vertex is halfway between the focus and the directrix, which is (-1/2, 0). Plugging these values into the standard form equation for a parabola, we get y^2 = -4x - 1. Graphing this equation with a window size of [-3, 3] by [-3, 3] shows a parabola opening to the left that intersects the directrix at x = 2, as expected. Choice B matches this graph.

Use a Graphing Utility to Graph the Conic Section with Focus