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:

$y=\dfrac{-42}{x}$

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.