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tia_tia [17]
3 years ago
14

Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1

Mathematics
1 answer:
geniusboy [140]3 years ago
5 0

Answer:

Step-by-step explanation:

eq. of directrix is y-1=0

let (x,y) be any point the parabola.

then\sqrt{ (x-6)^2+(y-2)^2}=\frac{y-1}{(-1)*2}

squaring

x²-12x+36+y²-4y+4=y²-2y+1

x²-12 x+40-1=4y-2y

2y=x²-12x+39=x²-12x+36+3

(x-6)²=2y-3

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Answer:

12/12

Step-by-step explanation:

6/12= 1/2

so 1/2+1/2 = One Whole and that the same thing as 12/12

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3 years ago
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3 years ago
Need help right now!!!!!
Irina18 [472]

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I just took the test and the correct answer is -6 is not in the domain of f g

Step-by-step explanation:

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3 years ago
Im trying to figure out how to find the length of an equilateral triangle
gulaghasi [49]

All 3 sides of an equilateral triangle are the same.

Set up an equation with two sides equaling each other and solve for n:

2n +15/4 = 7n

Subtract 2n from both sides:

15/4 = 5n

Divide both sides by 5:

n = (15/4) / 5

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7 0
4 years ago
Officials begin to release water from a full man-made lake at a rate that would empty the lake in 10 weeks, but a river that can
Romashka [77]

Answer:

It takes 20 weeks to empty the lake

Step-by-step explanation:

Some rate, let's call it R_{empty} empties the lake in 10 weeks and a river (with rate R_{river} can fill the lake in 20 weeks. The idea behind the solution of this type of problem is always set the rate to the same units. Let's see this:

R_{empty}=\frac{1\ lake}{10\ weeks} which implies that this rate empties 0.1 of the lake per week, thus, R_{empty}=0.1/week.

Using the same idea, we can obtain that the filling rate of the river is:

R_{river}=\frac{1\ lake}{20\ weeks} = 0.05 /week

Since both rates are acting at the same time, the total rate of flowing water (either in or out the lake) would be given by:

R_{total}=R_{empty}+R_{river}\\R_{total}= -0.1 + 0.05=-0.05/week, which means that the lake is being empty at a rate of -0.05 week and using the rule of three:

\frac{0.05}{1} = \frac{1}{total\ of\ weeks}  \\total\ of\ weeks = \frac{1}{0.05}=\frac{1}{\frac{1}{20} }\\  total\ of\ weeks = 20

Thus, It takes 20 weeks to empty the lake.

5 0
3 years ago
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