Question

Which is a true statement comparing the graphs of x^2/3^2 - y^2/4^2= 1 and y^2/3^2 - x^2/4^2 = 1?

The foci of both graphs are the same points.
The lengths of both transverse axes are the same.
The directrices of = 1 are horizontal while the directrices of = 1 are vertical.
The vertices of = 1 are on the y-axis while the vertices of = 1 are on the x-axis.

Answer 1

B

Explanation:

Answer 2

Answer: B) The lengths of both transverse axes are the same.

Step-by-step explanation: Given Hyperbola equations :

`(x^2)/(3^2)-(y^2)/(4^2)=1` and

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

First one :
`(x^2)/(3^2)-(y^2)/(4^2)=1` is a Horizontal Hyperbola.

a = 3 and 2a = 6.

Length of transverse axis = 6.

And second one :
`(y^2)/(3^2)-(x^2)/(4^2)=1` is a Vertical Hyperbola.

b=3 and 2b = 6

Length of transverse axis = 6.

The lengths of both transverse axes are the same.

Therefore, correct option is B option :

The lengths of both transverse axes are the same.