Question

PLEASE HELP HYPERBOLAS What is the length of the transverse axis ? (x-1)^2/25-(y+3)^2/9=1

Answer 1

Given equation of hyperbola is

$\frac{(x-1)^{2}}{25}-\frac{(y+3)^{2}}{9}=1$

Given hyperbola is the horizontal hyperbola

The standard form of the horizontal hyperbola is

$\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1$

When we compare these two equations, we get

h = 1, a = 5 , k = -3 and b = 3

Length of the transverse axis = 2a

Plug in the value of 'a' as 5

So,Length of the transverse axis = 2(5) = 10