IXL - Find the length of the transverse or conjugate axes of a hyperbola (Algebra 2 practice)

The graph shows a hyperbola. What is the length of its transverse axis?

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question

The graph shows a hyperbola. What is the length of its transverse axis?

key idea

A hyperbola that has a horizontal orientation opens right and left. A hyperbola that has a vertical orientation opens up and down.

The equation of a hyperbola that has a horizontal orientation in standard form is:

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The center is

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the vertices are

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and the co-vertices are

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Note that the vertices are on the hyperbola, but the co-vertices are not.

The transverse axis is the line segment with endpoints at the vertices and has length

The conjugate axis is the line segment with endpoints at the co-vertices and has length

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(

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(

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solution

The hyperbola opens right and left, so it has a horizontal orientation. This means the transverse axis is horizontal and the conjugate axis is vertical.

The length of the transverse axis is the distance between the two vertices, which is 4.

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Not feeling ready yet? These can help:

GG.2Find the vertices of a hyperbola

E.1Square roots of perfect squares

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