Question

which expression gives the length of the transverse axis of the hyperbola shown below?
a. 2(a + b)
b. a + b
c. 2(a - b)
d. a - b

Explanation:

Step1: Recall the definition of hyperbola

For a hyperbola, the difference of the distances from any point on the hyperbola to the two foci is constant. Let the distance from a point on the hyperbola to one focus be \(a\) and to the other focus be \(b\). The constant difference is \(a - b\).

Step2: Find the length of the transverse axis

The length of the transverse axis of a hyperbola is \(2\) times the constant difference. So the length is \(2(a - b)\).

Answer:

C. \(2(a - b)\)