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zmey [24]
3 years ago
11

.

Mathematics
2 answers:
serious [3.7K]3 years ago
7 0

Answer:

(C) (4,−8) and (4, 12)

Step-by-step explanation:

took the test

iren2701 [21]3 years ago
3 0

Answer:

(4,-8) and (4, 12)

Step-by-step explanation:

The equation of the hyperbola given is:

\frac{(y-2)^2}{64}-\frac{(x-4)^2}{36}=1

The general form of this hyperbola would be:

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

Thus, we can see that:

a^2 = 64

a = 8

and

b^2 = 36

b = 6

The distance from one focus to center is called "c", it goes by formula:

c^2=a^2+b^2

Let's find c:

c^2=8^2 + 6 ^2\\c^2=100\\c=10

This is a vertical hyperbola and the center is found from the x and y's on the numerator:

(y-2)^2 means y = 2

(x-4)^2 = x = 4

Center is (4, 2)

We go 10 units vertically up, so from y = 2 , ten units up makes it y = 12

x = 4 and y = 12

(4,12)

We go 10 units vertically down, so from y =2, ten units down makes it y = -8

x = 4 and y = -8

(4, -8)

<u>Foci coordinates:</u>

<u>(4,12) and (4,-8)</u>

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