5 seconds challenge
Geometry
Level
3
The eccentricity of hyperbola whose asymptotes are
and
is
The answer is 1.414.
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1 solution
Clearly the given lines are perpendicular to each other because product of their slopes is equal to -1.
Now, we know that a conic (particularly hyperbola) whose asymptotes are perpendicular is a RECTANGULAR HYPERBOLA.
BASIC DEFINITION: A hyperbola whose both the major & minor axes are equal is called a RECTANGULAR HYPERBOLA.
We know, e= a 2 b 2 + 1 where e, a & b are respectively the eccentricity and half the major & minor axes.
Now for a rectangular hyperbola, a=b
Therefore e = 2