Q18 of 23 Page 771

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

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]


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