AnswersPrecalculusEquations of Hyperbolas — QuizQuestion 4
4
QuizMultiple Choice

Equations of Hyperbolas — Quiz

Question 4 • Precalculus

Which is a true statement comparing the graphs of the fraction with numerator x squared and denominator 3 squared minus the fraction with numerator y squared and denominator 4 squared is equal to 1 and the fraction with numerator y squared and denominator 3 squared minus the fraction with numerator x squared and denominator 4 squared is equal to 1 ?

Answer
A
The vertices of the fraction with numerator x squared and denominator 3 squared minus the fraction with numerator y squared and denominator 4 squared is equal to 1 are on the y -axis while the vertices of the fraction with numerator y squared and denominator 3 squared minus the fraction with numerator x squared and denominator 4 squared is equal to 1 are on the x -axis.
B
The lengths of both transverse axes are the same.
C
The foci of both graphs are the same points.
D
The directrices of the fraction with numerator x squared and denominator 3 squared minus the fraction with numerator y squared and denominator 4 squared is equal to 1 are horizontal while the directrices of the fraction with numerator y squared and denominator 3 squared minus the fraction with numerator x squared and denominator 4 squared is equal to 1 are vertical.

Explanation

In each equation, the positive squared term has denominator 3², so the transverse-axis parameter is a = 3. The length of a hyperbola’s transverse axis is 2a, giving both graphs a transverse-axis length of 6. Their orientations differ, but their transverse-axis lengths are the same.

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