Question

MEDAL!

What is the length of the transverse axis of the hyperbola defined by the equation below?

(x-7)^2/7^2-(y+3)^2/4^2=1

(Picture below.)

Answer 1

the "traverse axis" for a hyperbola, is the axis where the hyperbola is opening towards, namely where the "a" component is...

anyhow... what's the POSITIVE fraction there? the fraction with the "x" variable or the one with the "y" variable?

Answer 2

the y variable!

Answer 3

hmmm... I should have said... what's the fraction with the POSITIVE SIGN in front of it

Answer 4

\(\bf \color{red}{\cfrac{(x-7)^2}{7^2}}-\cfrac{(y+3)^2}{4^2}=1\)

so, that's the axis where the hyperbola is opening towards, and thus that's the "traverse axis"

Answer 5

so the answer would be (x-7)^2/7^2?

Answer 6

in a hyperbola is usually on the left-hand side anyhow

well, you're only asked for the traverse axis, so is the x-axis, the hyperbola is opening horizontally