What is the length of the conjugate axis?

ANSWER

The length of the conjugate axis is 6 units.

EXPLANATION

The given hyperbola has equation:

[tex] \frac{(x - 1)^{2} }{25} - \frac{ {(y + 3)}^{2} }{9} = 1[/tex]

We can rewrite this equation in the form:

[tex]\frac{(x - 1)^{2} }{ {5}^{2} } - \frac{ {(y + 3)}^{2} }{ {3}^{2} } = 1[/tex]

We compare this equation to:

[tex]\frac{(x - h)^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]

This implies that;

[tex]a = 5[/tex]

and

[tex]b = 3[/tex]

The length of the conjugate axis of a hyperbola is

[tex] = 2b[/tex]

Substitute b=3 to obtain;

[tex] = 2 \times 3[/tex]

[tex] = 6[/tex]