Question

Which of the following is not an asymptote of the hyperbola xy = -42? y = 0 x = 0 y = x

Answer 1

Given:

The equation of the hyperbola is:

`xy=-42`

To find:

The the equation which is not an asymptote of the hyperbola.

Solution:

We have,

`xy=-42`

It can be written as:

`y=(-42)/(x)`

Equating denominator and 0, we get

`x=0`

So, the vertical asymptotic is
`x=0`.

The degree of numerator is 0 and the degree of denominator is 1.

Since the degree of numerator is greater that the degree of denominator, therefore the horizontal asymptote is
`y=0` and there is no oblique asymptote.

Therefore,
`y=x` is not an asymptote of the given hyperbola and the correct option is C.