# In a Hyperbola - The Triangle formed by an latus rectam with its farthest vertex is equilateral then find its ecentricity

### Asked by Malavika Umesh | 1st May, 2015, 01:06: PM

Expert Answer:

### Consider equation of a hyperbola in standad form.
Eccentricity 'e' is given by
The coodinates of ends of latus rectum of one half of the hyperbola are
The coordinates of the vertex farther from the latus rectum are
Since the triangle formed by these points is an equilateral triangle, equating the side lengths formed by these vertices we get
Adding to both sides of the above equation, we get
From (1) and (2), we get
Taking only the posiive sign, as 'e' can not be negative, we get

### Answered by satyajit samal | 3rd May, 2015, 10:04: AM

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