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sukhopar [10]
2 years ago
14

Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7

Mathematics
1 answer:
shtirl [24]2 years ago
4 0

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

y=\dfrac{1}{4p}(x-h)^2+k                  ...(i)

Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.

The focus of the parabola is at (6,-4).

(h,k+p)=(6,-4)

On comparing both sides, we get

h=6

k+p=-4                            ...(ii)

Directrix at y=-7. So,

k-p=-7                            ...(iii)

Adding (ii) and (iii), we get

2k=-11

k=\dfrac{-11}{2}

k=-5.5

Putting k=-5.5 in (ii), we get

-5.5+p=-4

p=-4+5.5

p=1.5

Putting h=6, k=-5.5,p=1.5 in (i), we get

y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)

y=\dfrac{1}{6}(x-6)^2-5.5

Therefore, the equation of the parabola is y=\dfrac{1}{6}(x-6)^2-5.5.

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3 years ago
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
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Read 2 more answers
Compute the standard deviation for the set of data.<br><br> 13.3, 14.3, 15.3, 16.3, 17.3
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<h3>Answer: Choice A)  sqrt(2)</h3>

==========================================

Explanation:

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Then divide by 5 as there are n = 5 values in the set given

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-------------

Subtract the mean from each value to get this list of differences

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-------------

Square each result from the previous section

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Then add up those results

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Divide the sum of the squared differences by n = 5 to get 10/5 = 2

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The population standard deviation is the square root of this, so we get sqrt(2) as our final answer.

------------

Side note: This data set was fairly small, so computing the standard deviation by hand wasnt too painful. When it comes to larger data sets, it is smarter to use a spreadsheet program to easily calculate the answer. The drawback is that you wont be able to get an exact answer in terms of radicals (then again you could always use a CAS, which stands for "computer algebra system").

6 0
3 years ago
(1 point) Let y=ex/5. Find the differential dy when x=2 and dx=0.2 Find the differential dy when x=2 and dx=0.01
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\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}

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