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likoan [24]
3 years ago
14

Write the equation for the hyperbola with foci (–12, 6), (6, 6) and vertices (–10, 6), (4, 6).

Mathematics
1 answer:
fomenos3 years ago
7 0

Answer:

\frac{(x--3)^2}{49} -\frac{(y-6)^2}{32}=1

Step-by-step explanation:

The standard equation of a horizontal hyperbola with center (h,k) is

\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1

The given hyperbola has vertices at (–10, 6) and (4, 6).

The length of its major axis is 2a=|4--10|.

\implies 2a=|14|

\implies 2a=14

\implies a=7

The center is the midpoint of the vertices (–10, 6) and (4, 6).

The center is (\frac{-10+4}{2},\frac{6+6}{2}=(-3,6)

We need to use the relation a^2+b^2=c^2 to find b^2.

The c-value is the distance from the center (-3,6) to one of the foci (6,6)

c=|6--3|=9

\implies 7^2+b^2=9^2

\implies b^2=9^2-7^2

\implies b^2=81-49

\implies b^2=32

We substitute these values into the standard equation of the hyperbola to obtain:

\frac{(x--3)^2}{7^2} - \frac{(y-6)^2}{32}=1

\frac{(x+3)^2}{49} -\frac{(y-6)^2}{32}=1

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2 years ago
Which equation represents the line that passes through the points (–3, 7) and (9, –1)?
galben [10]

Answer:

Step-by-step explanation:

first, we find the slope

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(-3,7)....x1 = -3 and y1 = 7

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now we sub

slope(m) = (-1 - 7) / (9 - (-3) = -8 / (9 + 3) = -8 / 12 reduces to - 2/3

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use either of ur points...I will use (-3,7)...x = -3 and y = 7

now we sub and find b, the y intercept

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7 0
3 years ago
Read 2 more answers
What is y-value when x equals -12? y =-200 - 6(x)
Arada [10]
Hi,

Solving:

x = - 12 \\ y = - 200 - 6( x) \\ y = - 200 - 6( - 12) \\ y = - 200 + 72 = \underline{ \underline{ - 128}}

Answer: y = -128

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r3t40
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3 years ago
If AB=BC,AB=4=4x-2,andBC=3x+3,fine the length of AB
laila [671]

Answer:

18

Step-by-step explanation:

First, I'm assuming AB=4=4x-2 was a typo and it's supposed to be AB = 4x - 2

AB=BC

AB = 4x - 2 BC = 3x + 3

4x - 2 = 3x + 3

Solve for x Add 2 to each side

4x - 2 = 3x + 3

4x - 2 + 2 = 3x + 3 + 2

4x = 3x + 5 Subtract 3x from each side.

4x - 3x = 3x- 3x + 5

4x - 3x = 5

x = 5

Now plug back in to the original equations

AB = 4x - 2                  BC = 3x + 3

AB = 4 (5) - 2               BC = 3(5) + 3

AB = 20 - 2                  BC = 15 + 3

AB = 18                        BC = 18

So AB is 18

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