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babymother [125]
3 years ago
12

The center of a hyperbola is (−4,3) , and one vertex is (−4,7) . The slope of one of the asymptotes is 2.

Mathematics
2 answers:
Monica [59]3 years ago
7 0

Answer:

The answer to your question is below

Step-by-step explanation:

C (-4, 3)

V (-4, 7)

asymptotes = 2 = \frac{b}{a}

- This is a vertical hyperbola, the equation is

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

slope = 2

a is the distance from the center to the vertex = 4

b = 2(4) = 8

       \frac{(y - 3)^{2} }{4^{2} } + \frac{(x + 4)^{2} }{8^{2} } = 1

       \frac{(y - 3)^{2} }{16} + \frac{(x + 4)^{2} }{64} = 1

Ne4ueva [31]3 years ago
5 0

Answer:

\frac{(x+4)^{2}}{4} - \frac{(y-3)^{2}}{16} = 1

Step-by-step explanation:

The hyperbola centered at (h,k) has the following expression:

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

Where a and b are the length of the horizontal and vertical semi-axes, respectively.

Since the center and one vertex share the same vertical component (x=-4), it is easy to conclude that hyperbola has a vertical configuration (b > a). The distance between the center and the known vertex is equal to the length of the vertical semi-axis. Therefore:

b = 4

The slope of the hyperbola is given by the following relationship:

\frac{b}{a} = 2

The length of the horizontal semi-axis is:

a = \frac{b}{2}

a = 2

The standard form of the equation of the hyperbola is:

\frac{(x+4)^{2}}{4} - \frac{(y-3)^{2}}{16} = 1

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