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Unformatted text preview: meter of the parabola is |4p|,
which, in light of Equation 7.2, is easy to ﬁnd. In our last example, for instance, when graphing
(x + 1)2 = −8(y − 3), we can use the fact that the focal diameter is | − 8| = 8, which means the
parabola is 8 units wide at the focus, to help generate a more accurate graph by plotting points 4
units to the left and right of the focus.
Example 7.3.2. Find the standard form of the parabola with focus (2, 1) and directrix y = −4.
Solution. Sketching the data yields,
3 No, I’m not making this up.
Consider this an exercise to show what follows. 410 Hooked on Conics
−1 1 2 3
The vertex lies on this vertical line
midway between the focus and the directrix −2
−3 From the diagram, we see the parabola opens upwards. (Take a moment to think about it if you
don’t see that immediately.) Hence, the vertex lies below the focus and has an x-coordinate of 2.
To ﬁnd the y -coordinate, we note that the distance from the focus to the directrix is 1 − (−4) = 5,
which means the vertex lie...
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