To nd the foci we need c 3 1 9 a2 b2 lie on the

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Unformatted text preview: s 5/2 units (halfway) below the focus. Starting at (2, 1) and moving down 5/2 units leaves us at (2, −3/2), which is our vertex. Since the parabola opens upwards, we know p is positive. Thus p = 5/2. Plugging all of this data into Equation 7.2 give us (x − 2)2 = 4 5 2 (x − 2)2 = 10 y + y− − 3 2 3 2 If we interchange the roles of x and y , we can produce ‘horizontal’ parabolas: parabolas which open to the left or to the right. The directrices4 of such animals would be vertical lines and the focus would either lie to the left or to the right of the vertex. A typical ‘horizontal’ parabola is sketched below. D V 4 plural of ‘directrix’ F 7.3 Parabolas 411 Equation 7.3. The Standard Equation of a Horizontal Parabola: The equation of a (horizontal) parabola with vertex (h, k ) and focal length |p| is (y − k )2 = 4p(x − h) If p > 0, the parabola opens to the right; if p < 0, it opens to the left. Example 7.3.3. Graph (y − 2)2 = 12(x + 1). Find the vertex, focus, and directrix. Solution. W...
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