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lesya692 [45]
1 year ago
15

Write a equation of a hyperbola given the foci and the asymptotes

Mathematics
1 answer:
professor190 [17]1 year ago
3 0

Solution:

The standard equation of a hyperbola is expressed as

\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\text{ \lparen parallel to the x-axis\rparen} \\ \frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ \lparen parallel to the y-axis\rparen} \end{gathered}

Given that the hyperbola has its foci at (0,-15) and (0, 15), this implies that the hyperbola is parallel to the y-axis.

Thus, the equation will be expressed in the form:

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

The asymptote of n hyperbola is expressed as

y=\pm\frac{a}{b}(x-h)+k

Given that the asymptotes are

y=\frac{3}{4}x\text{ and y=-}\frac{3}{4}x

This implies that

a=3,\text{ and b=4}

To evaluate the value of h and k,

undefined

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