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2 years ago

Zoe supplies costumes to a number of theater companies. She

Mathematics

1 answer:

KengaRu [80]2 years ago

6 0

Answer:3

Step-by-step explanation:

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Write the equation of the hyperbola centered at the origin, with a focus at (10, 0) and directrix at x = 125/10

vladimir1956 [14]

Answer:

the equation of the hyperbola centered at the origin is

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

$\frac{x^2}{\left(5\sqrt{5}\right)^2}-\frac{y^2}{\left(5i\right)^2}=1$

Step-by-step explanation:

For a right-left facing hyperbola, the Foci (focus points) are defined:

$\left(h+c,\:k\right),\:\left(h-c,\:k\right)$

where $c=\sqrt{a^2+b^2}$ is the distance form the center (h, k) to a focus.

So, the standard equation will be

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

As the equation of directrix at x = 125/10

Focus at (10, 0)

As the directrix is the line is

$x=\frac{a^2}{c}$

As c = 10, and x = 125/10

So,

$\:x\times c=a^2$

$\sqrt{x\times \:c}=a$

$\sqrt{\frac{125}{10}\times \:10}=a$

$5\sqrt{5}=a$

$a^2+b^2=c^2$

$b^2=c^2-a^2$

$b=\sqrt{c^2-a^2}$

$b=\sqrt{\left(10\right)^2-\left(5\sqrt{5}\right)^2}$

$b=\sqrt{100-125}$

$b=\sqrt{-25}$

$b=\sqrt{-1}\sqrt{25}$

$\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i$

$b=\sqrt{25}i$

$b=5i$

Therefore, the equation of the hyperbola centered at the origin is

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

$\frac{x^2}{\left(5\sqrt{5}\right)^2}-\frac{y^2}{\left(5i\right)^2}=1$

Keywords: hyperbola, directrex, foci, equation of hyperbola

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7 0

3 years ago

PLEASE HELP quick ………

Anit [1.1K]

Answer:

Step-by-step explanation:

1/2 x base x height

In this problem: (It's times 2 because I split it up into 2 triangles.)

1/2 x 10 x 5 x 2 =

hope this helps

have a good day

7 0

2 years ago

What is the correct value of 3x + 2 for x = 5?

Reptile [31]

Answer:

Step-by-step explanation:

3x + 2

x = 5

3x + 2

3(5) + 2

15 + 2

5 0

2 years ago

Read 2 more answers

Can you guys helps with these two answers please?

aalyn [17]

7^1 (-1x-1=1)

5^3 (2+4-3=3)

4 0

2 years ago

An image point of a transformation has coordinates Y'(2, -4). If the pre-image point had coordinates Y(6, -12), what was the tra

docker41 [41]

Answer:

(-4,-8)

Step-by-step explanation:

Sorry if i get it wrong if im really off that much plsexplain to me how to do this

3 0

3 years ago