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# Foci and asymptotes of a hyperbola

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A hyperbola is given the equation x^2/25 - y^2/9 = 1

A) Find the coordinates of the foci and the equations of the asymptotes.

B) Find the point of intersection with the line y=4-x

c) Graph the hyperbola, the line, and the point of intersection.
Please explain how to graph this because I dont understand it and second which equation should I use:

x^2/b^2 - y^2 /a^2 = 1

or x^2/ a^2 - y^2 /b^2 =1

and why???

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#### Solution Preview

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Hyperbola:

A hyperbola is given the equation x^2/25 - y^2/9 = 1

a) Find the coordinates of the foci and the equations of the asymptotes.

If the hyperbola is given by the following general equation,
x2/a2 - y2/b2 = 1
then the foci are given by (c,0) and (-c,0) where c = sqrt(a2+b2)
Here a = 5, b = 3
Forci (±sqrt(34), 0)
The equation of the ...

#### Solution Summary

Answer is in a 3-page word document. I have provided very detailed step by step solution along with a graph. Answer is easy to understand.

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