Question

The difference of the focal distances of any point on the hyperbola is equal to

Options

• length of the conjugate axis

•  eccentricity

• length of the transverse axis

• Latus-rectum

Answer 1

length of the transverse axis

Let  \[P\left( x, y \right)\] be any point on the hyperbola, and  \[S, S'\] be the focus with coordinates  \[\left( \pm ae, 0 \right)\] .

⇒ \[S'P - SP = 2a\] 

Thus, the difference of the focal distances of any point on the hyperbola is equal to the length of the transverse axis.