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kipiarov [429]
3 years ago
7

Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8

Mathematics
1 answer:
Gekata [30.6K]3 years ago
3 0
First, let (x,y) be a point in our parabola. Since we know that the focus of our parabola is  the point (0,8), we are going to use the distance formula to find the distance between the two points:
\sqrt{(x-0)^{2}+(y-8)^{2}}

Next, we are going to find the distance between the directrix and the point in our parabola. Remember that the distance between a point (x,y) of a parabola and its directrix, y=c, is: |y-c|. Since our directrix is y=-8, the distance to our point will be:
|y-(-8)|
|y+8|

Now, we are going to equate those two distances, and square them to get rid of the square root and the absolute value:
\sqrt{(x-0)^{2}+(y-8)^{2}}=|y+8|
(\sqrt{(x-0)^{2}+(y-8)^{2}})^{2}=|y+8|^{2}
(x-0)^{2}+(y-8)^{2}=y+8

Finally, we can expand and solve for y:
x^2+y^2-16y+64=y^2+16y+64
x^{2}-16y=16y
32y=x^{2}
y= \frac{1}{32} x^2

We can conclude that t<span>he standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is </span>y= \frac{1}{32} x^{2}

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This conclusion can be made from the prompt.

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A 10 ounce can of peaches cost $2.40 in a 25 ounce can of peaches cost $4.80 what is the unit price of the 25 ounce can of peach
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The average wind speed at a local weather station is 34.8 miles per hour. The highest speed ever recorded the stations 318.0 mil
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Answer:

Difference = 283.2\ miles/hour

Step-by-step explanation:

Given

Average\ Speed = 34.8\ miles/hour

Highest\ Speed = 318.0\ miles/hour

Required

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Difference = Highest\ Speed - Average\ Speed

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<em>Hence, the highest speed is 283.2 miles/hour faster than the average speed</em>

3 0
3 years ago
Week 5 Quiz - Saving (15pts) 1. If the interest rate on a savings account is 0.01%, approximately how much money do you need to
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4 0
3 years ago
hich function has a range of {y|y ≤ 5}? f(x) = (x – 4)2 + 5 f(x) = –(x – 4)2 + 5 f(x) = (x – 5)2 + 4 f(x) = –(x – 5)2 + 4
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Answer:

f(x)=-(x-4)^2+5

Step-by-step explanation:

The function f(x)=-(x-4)^2+5 has  the vertex at (4,5).


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The highest y-value is the y-coordinate of the vertex which is 5.


Therefore the range is {y|y\le 5}


Therefore the correct answer is B.


6 0
3 years ago
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