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gregori [183]
3 years ago
14

Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)

Mathematics
2 answers:
sergeinik [125]3 years ago
8 0

Answer:

Hope this helps :)

Step-by-step explanation:

Nitella [24]3 years ago
5 0

The equation of a hyperbola is:

(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1

 

So what we have to do is to look for the values of the variables:

<span>For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9</span>

<span>
c = 7 (distance from center to vertices; given from the foci)
c^2 = 49</span>

 

<span>By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2 </span>

<span>b^2 =  49 – 9</span>

<span>b^2  = 40

</span>

Therefore the equation of the hyperbola is:

<span>(x^2 / 9) – (y^2 / 40) = 1</span>

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