Since a 5 and the slope of the line y 2x is 2 we have

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Unformatted text preview: ocus is 2 units below the vertex. If we start at (−1, 3) and move down 2 units, we arrive at the focus (−1, 1). The directrix, then, is 2 units above the vertex and if we move 2 units up from (−1, 3), we’d be on the horizontal line y = 5. 7.3 Parabolas 409 y 5 4 3 2 1 −6 −5 −4 −3 −2 −1 −1 1 2 3 4 x −2 Of all of the information requested in the previous example, only the vertex is part of the graph of the parabola. So in order to get a sense of the actual shape of the graph, we need some more information. While we could plot a few points randomly, a more useful measure of how wide a parabola opens is the length of the parabola’s latus rectum.2 The latus rectum of a parabola is the line segment parallel to the directrix which contains the focus. The endpoints of the latus rectum are, then, two points on ‘opposite’ sides of the parabola. Graphically, we have the following. the latus rectum F V D It turns out3 that the length of the latus rectum, called the focal dia...
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