Question
Download Solution PDFFind the length of the latus rectum of the hyperbola x2 - y2 = 1 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The properties of a rectangular hyperbola
- Its centre is given by: (0, 0)
- Its foci are given by: (- ae, 0) and (ae, 0)
- Its vertices are given by: (- a, 0) and (a, 0)
- Its eccentricity is given by:
- Length of transverse axis = 2a and its equation is y = 0.
- Length of conjugate axis = 2b and its equation is x = 0.
- Length of its latus rectum is given by:
CALCULATION:
Given: Equation of hyperbola is x2 - y2 = 1
As we can see that, the given hyperbola is a horizontal hyperbola.
So, by comparing the given equation of hyperbola with
⇒ a = 1 and b = 1
As we know that, length of latus rectum of a hyperbola is given by
So, the length of latus rectum of given hyperbola is 2 units.
Hence, option D is the correct answer.
Last updated on Jul 4, 2025
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