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AlekseyPX
1 year ago
5

The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0, 4). One branch has a vertex at (0, 10) a

nd its respective focus at (0, 14). Which equation represents the comet's orbit?

Mathematics
1 answer:
Anuta_ua [19.1K]1 year ago
6 0

Remember that

If the given coordinates of the vertices and foci have the form (0,10) and (0,14)

then

the transverse axis is the y-axis

so

the equation is of the form

(y-k)^2/a^2-(x-h)^2/b^2=1

In this problem

center (h,k) is equal to (0,4)

(0,a-k)) is equal to (0,10)

a=10-4=6

(0,c-k) is equal to (0,14)

c=14-4=10

Find out the value of b

b^2=c^2-a^2

b^2=10^2-6^2

b^2=64

therefore

the equation is equal to

<h2>(y-4)^2/36-x^2/64=1</h2><h2>the answer is option A</h2>
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Looking at the problem, you see both .6 and .4 are placed to the right of the decimal, otherwise known as the tenths place (1/10). 

Looking at 1.9, you see you have one number (1) placed to the left of the decimal, the ones place, and another number placed to the right of the decimal (9), in the tenths place. 

Well, this is simple. You can look and see that your multiplying fractions against a whole number, which will of course make this whole number even smaller. By how much though??

Well, you can really tell this by looking at how MANY numbers are behind the decimal. You have .9, .4, and .6

That's 3 numbers behind the decimal place. This may not help you solve the problem itself, but this tells you here (ignoring the 1, that will be taken out immediately while solving and turned into a 0) that you will have 3 numbers placed from the tenths place all the way to the thousandths place.

Basically, this tells you that you'll have three decimal places to the right of the decimal. 

As for rewriting your problem to better show this, that's simple too.

All you have to do is simple multiplication, just in the tenths place. How? You know that 6*4 (referring to .6 and .4) is 24, that means that .6*.4 will be .24

How does this support your answer before? .24 has TWO numbers to the right of the decimal. That's TWO decimal places. With the .9 in 1.9, that's still THREE decimal places to the right of the decimal, and your answer would be the same.

So, here's it re-written.
1.9*.24=X

~Hope this helps!


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