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1 answer:
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Answer:
- y = 1/16(x -2)^2 -1
- x = -1/12(y +3)^2 -2
Step-by-step explanation:
1. For a parabola with vertex (h, k) that opens upward, the equation can be written ...
y = 1/(4p)(x -h)^2 +k
where 4p is the focal width. Here, that is 16, and (h, k) = (2, -1), so the equation is ...
y = 1/16(x -2)^2 -1
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2. The focal width is 4 times the distance from the focus to the directrix, so for this one we have ...
4p = 4(2 -5) = -12
Because the parabola opens sideways, the roles of x and y in the equation are swapped. The equation for this parabola is ...
x = 1/(4p)(y -k)^2 +h . . . . . . . for vertex (h, k) and focal width 4p
x = -1/12(y +3)^2 +2
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The graph shows the two parabolas and their equations. The dashed lines are the focal width and the directrix.
