Find the equation of the hyperbola, the length of whose latus rectum is 4 and the eccentricity is 3.

Question

Philoid · Accepted Answer

Given: The length of latus rectum is 4, and the eccentricity is 3

Need to find: The equation of the hyperbola.

Let, the equation of the hyperbola be:

The length of the latus rectum is 4 units.

Therefore, ⇒ ---- (1)

And also given, the eccentricity, e = 3

We know that,

Therefore,

⇒

⇒ [Squaring both sides]

⇒

⇒ [From (1)]

⇒

Therefore,

So, the equation of the hyperbola is,

⇒ ⇒ [Answer]