Chapter 12 . 12-5 Parabolas. Objectives . Write the standard equation of a parabola and its axis of symmetry. Graph a parabola and identify its focus, directrix , and axis of symmetry. parabolas.
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Write the standard equation of a parabola and its axis of symmetry.
Graph a parabola and identify its focus, directrix, and axis of symmetry.
Substitute (2, 4) for (x1, y1) and (x, –4) for (x2, y2).
(x – 2)2 + (y – 4)2 = (y + 4)2
Square both sides.
(x – 2)2 + y2 – 8y + 16 = y2 + 8y + 16
Subtract y2 and 16 from both sides.
(x – 2)2 = 16y
Add 8y to both sides.
Solve for y
y = 1/4p x2 with p < 0.
x = 1/24 y2
x of a Parabola= y2,
x = y2.
The equation for the cross section is in the form
so 4p = 132 and p = 33. The focus
should be 33 inches from the vertex of the cross section. Therefore, the feedhorn should be 33 inches long.Example 4: Using the Equation of a Parabola