Convert fraction with numerator 7 and denominator 8 to a decimal.
1 answer:
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You plot the point of the focus and the directrix on the graph to determine where the parabola opens.
We are provided the general forms of parabola according to its opening if:
it opens upward: (x - h)<span>² = 4a(y - k)
</span>it opens downward: (x - h)<span>² = -4a(y - k)
where "h" and "k" are the coordinates of the vertex, and "a" is the focal length from the focus to the vertex.
As you plot, the directrix y = 9 is a horizontal line, and the focus at (0,-9) is below that directrix. So, it means that the parabola opens downward (and not upward because the parabola must not touch to the directrix).</span> Next, identity the vertex (h,k). Note that the vertex is the midpoint between the focus and the point of the directrix. So the vertex is (0,0). Then, the focal length "a" is 9.
Hence, the equation is
(x - 0)<span>² = -4(9)(y - 0)
x</span><span>² = -36y</span>
We are provided the general forms of parabola according to its opening if:
it opens upward: (x - h)<span>² = 4a(y - k)
</span>it opens downward: (x - h)<span>² = -4a(y - k)
where "h" and "k" are the coordinates of the vertex, and "a" is the focal length from the focus to the vertex.
As you plot, the directrix y = 9 is a horizontal line, and the focus at (0,-9) is below that directrix. So, it means that the parabola opens downward (and not upward because the parabola must not touch to the directrix).</span> Next, identity the vertex (h,k). Note that the vertex is the midpoint between the focus and the point of the directrix. So the vertex is (0,0). Then, the focal length "a" is 9.
Hence, the equation is
(x - 0)<span>² = -4(9)(y - 0)
x</span><span>² = -36y</span>
Answer: Choice A) There must be a vertical asymptote at x = c
Explanation:
The first limit says that as x approaches c from the left side, the f(x) or y values approach negative infinity. So the graph goes down forever as x approaches this c value from the left side.
The limit means that as x approaches c from the right side, the y values head off to positive infinity.
Either of these facts are enough to conclude that we have a vertical asymptote at x = c. We can think of it like an electric fence in which we can get closer to, but not actually touch it.