Which expression gives the length of the transverse axis of the hyperbola shown below?A.B.x + yC.x - yD.SUBMITarrow_backPREVIOUS

Break Down the Problem

1. Identify the standard form of a hyperbola and understand its features, particularly the transverse axis.
2. Recognize how the given expressions relate to the characteristics of a hyperbola.

Relevant Concepts

The transverse axis of a hyperbola is the segment that connects the two vertices on the hyperbola. For the standard forms of hyperbolas:

• Horizontal hyperbola: $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$
• Vertical hyperbola: $\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1$

Where:

• $2a$ is the length of the transverse axis.

Analysis and Detail

In hyperbolas, the transverse axis length is defined by the term $a$ in relation to the vertices of the hyperbola. We need to evaluate the given expressions:

1. A. $B.x + y$ - This does not align with the standard hyperbola form.
2. B. $C.x - y$ - Also doesn't suggest a direct correlation to the transverse axis.
3. C. $x - y$ - Similar to above, this expression does not relate to the length of the transverse axis.

Verify and Summarize

From the analysis of the provided expressions $(A, B, C)$, none seem to correctly represent the length of the transverse axis for the hyperbola in standard form. In standard cases, the expression would typically involve $a$.

Final Answer

None of the provided expressions (A, B, C) accurately represent the length of the transverse axis of the hyperbola.