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

Given:

The equation of the hyperbola is:

To find:

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

Solution:

We have,

It can be written as:

Equating denominator and 0, we get

So, the vertical asymptotic is .

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 and there is no oblique asymptote.

Therefore, is not an asymptote of the given hyperbola and the correct option is C.

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