If two tangents can be drawn to the different branches of hyperbolax21−y24=1 f

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If two tangents can be drawn to the different branches of hyperbola

\frac{x^{2}}{1} - \frac{y^{2}}{4} = 1

from the paint

(α, α^{2})

, then

Options:

A . αϵ(−2,0)

B . αϵ(−3,0)

C . αϵ(−∞,−2)

D . αϵ(−∞,−3)

Answer: Option C
:
C
Given that,

\frac{x^{2}}{1} - \frac{y^{2}}{4} = 1

If Two Tangents Can Be Drawn To The Different Branches Of Hy...

Since,

(α, α^{2})

lie on the parabola

y = x^{2}

, then

(α, α^{2})

must lie between the asymptotes of hyperbola

\frac{x^{2}}{1} - \frac{y^{2}}{4} = 1

in 1st and 2nd quadrants.
So, the asymptotes are

y = \pm 2 x

∴

2 α < α^{2}

\Rightarrow

α < 0 o r α > 2

and

- 2 α < α^{2}

α < - 2 o r - 2 α < 0

∴

α ϵ (- \infty, - 2) o r (2, \infty)

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