Question

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

Answer 1

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.