Question
Download Solution PDFFind the equation of the hyperbola whose vertices are (0, ± 3) and the eccentricity is 4/3 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The properties of a vertical hyperbola
- Its centre is given by: (0, 0)
- Its foci are given by: (0, - ae) and (0, ae)
- Its vertices are given by: (0, - a) and (0, a)
- Its eccentricity is given by:
- Length of transverse axis = 2a and its equation is x = 0.
- Length of conjugate axis = 2b and its equation is y = 0.
- Length of its latus rectum is given by:
CALCULATION:
Here, we have to find the equation of the hyperbola whose vertices are (0, ± 3) and the eccentricity is 4/3
By comparing the vertices (0, ± 3) with (0, ± a) we get
⇒ a = 3
As we know that,
⇒ a2e2 = a2 + b2
⇒ 16 = 9 + b2
⇒ b2 = 7
so, the equation of the hyperbola is
Hence, option C is the correct answer.
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