The graph of this equation has two asymptotes, while a parabola has no asymptotes. Of course, that does not make this a hyperbola (although it is), but we are given only the two choices.
You might otherwise put it in general form and check the discriminant.
y = 1/x
xy - 1 = 0
discriminant = (1)² - 4(0)(0) = 1
The discriminant of a parabola is zero.
The discriminant of a hyperbola is greater than zero.
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Verified answer
The graph of this equation has two asymptotes, while a parabola has no asymptotes. Of course, that does not make this a hyperbola (although it is), but we are given only the two choices.
You might otherwise put it in general form and check the discriminant.
y = 1/x
xy - 1 = 0
discriminant = (1)² - 4(0)(0) = 1
The discriminant of a parabola is zero.
The discriminant of a hyperbola is greater than zero.
it is a hyperbola
It is considered a "rectangular hyperbola."