Question

What is the length of the transverse axis?
((y-2)^2/16)-((x+1)^2/144)=1

Answer 1

the main formula is (y-h)² /b² - (x-k)²/a² = 1
the transverse axis is vertical and can be found by 2b
b² = 16, so b=4, and the measure is D=2b=8

Answer 2

The length of the transverse axis is 8

Explanation:

We have been given the equation of hyperbola

`((y-2)^2)/(16)-((x+1)^2)/(144)=1`

We can rewrite this equation as

`((y-2)^2)/(4^2)-((x+1)^2)/(12^2)=1`

Comparing this equation with the standard equation of hyperbola having vertical transverse axis is

`((y-k)^2)/(a^2)-((x-h)^2)/(b^2)=1`

h = -1

k= -2

a = 4

b = 12

The length of the transverse axis is 2a = 2×4 =8