Question

what is the length of latus rectum of an hyperbola ?

Answer 1

A spacecraft can use the gravity of a planet to alter its path and propel it at high speed away from the planet and back out into space using a technique called "gravitational slingshot".

If this happens, then the path of the spacecraft is a hyperbola

Answer 2

Step-by-step explanation:

Length of latus rectum of a hyperbola is 2b2a where a is the half of the distance between two vertex of kthe hyperbola.

Latis rectum =2b2a=103

or, b2=5a3 ..(1)

In case of hyperbola.

b2=a2(e2−1) ...(2)

Putting value b2from equatin (1) and e=13−−√3 in equation (2).

5a3=a2(139−1)

or, 5a3=4a29

⇒ 4a2−15a=0 or a(4−15a)=0

a≠0, hence, a=154

Length of transverse axis = 2a = 2×154=152