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What are the asymptotes of the hyperbola given by the equation 1296y2 - x² = 81?

1 Answer

4 votes

Answer: y =
(x)/(36), y = -
(x)/(36)

Explanation:

Every hyperbola has two asymptotes. We can use the formula to solve for these asymptotes. We are given the equation 1296y² - x² = 81.


\displaystyle y=\pm (a)/(b) (x-h)+k

We will substitute our values into the formula. (h, k), the center of the hyperbola, is at (0, 0) here.


\displaystyle y=\pm ((1)/(4) )/(9) (x-0)+0

Now, we can simplify by multiplying, distributing, subtracting, adding, etc.


\displaystyle y=\pm (1)/(36)(x-0)+0


\displaystyle y=\pm (1)/(36)x-0+0


\displaystyle y=\pm (1)/(36)x


\displaystyle y=\pm (x)/(36)


\displaystyle y= (x)/(36) \;\;and\;\;y= -(x)/(36)

I have attached a graph of this below. The hyperbola is graphed in blue with the asymptotes graphed in red.

What are the asymptotes of the hyperbola given by the equation 1296y2 - x² = 81?-example-1
User Giri
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