Hyperbola

If PQ is a double ordinate of the Hyperbola x2/a2 - y2/b2 = 1 such that OPQ is an equilateral triangle ,O being the centre of the hyperbola..Then the range of eccentricity 'e' of the hyperbola is????

1 Answers

1357
Manish Shankar ·

Take a point of hyperbola as (asecθ,btanθ)

Now this point has a slope of tan30 from origin.

tan30=btanθ/asecθ=bsinθ/a=1/√3

b/a=1/√3sinθ

e2=1+(b/a)2=1+1/3sin2θ

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