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If form (alpha,beta), two tangents are d...

If form `(alpha,beta),` two tangents are drawn to circle `x^2+y^2=4` so that slopes of tangents are in the ratio `1:2` and `f(x)=alpha^2x^2+12 x=(beta^2)/4,` then `f(x)>0AAx in R` Locus of `(alpha^2,beta^2)` is a hyperbola least positive integral value of `alpha` is 1 eccentricity of locus of `(alpha^2,beta^2)` is `sqrt(2)`

A

`(2sqrt2, 2sqrt2)`

B

`((2sqrt2)/(sqrt3),(2sqrt2)/(sqrt3))`

C

(2, 2)

D

none of these

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The correct Answer is:
A
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