"Let the eccentricity of the hyperbola $H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$ be $\sqrt {{5 \over 2}}$ and length of its latus rectum be $6\sqrt 2$. If $y = 2x + c$ is a tangent to the hyperbola H, then the value of c2 is equal to :"

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$$1 + {{{b^2}} \over {{a^2}}} = {5 \over 2} \Rightarrow {{{b^2}} \over {{a^2}}} = {3 \over 2}$$

${{2{b^2}} \over a} = 6\sqrt 2 \Rightarrow 2.\,{3 \over 2}.\,a = 6\sqrt 2$

$\Rightarrow a = 2\sqrt 2 ,\,{b^2} = 12$

${c^2} = {a^2}{m^2} - {b^2} = 8.4 - 12 = 20$

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Let the eccentricity of the hyperbola $H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$ be $\sqrt {{5 \over 2}}$ and length of its latus rectum be $6\sqrt 2$. If $y = 2x + c$ is a tangent to the hyperbola H, then the value of c² is equal to :

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Let the eccentricity of the hyperbola $H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$ be $\sqrt {{5 \over 2}}$ and length of its latus rectum be $6\sqrt 2$. If $y = 2x + c$ is a tangent to the hyperbola H, then the value of c2 is equal to :

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Let the eccentricity of the hyperbola $H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$ be $\sqrt {{5 \over 2}}$ and length of its latus rectum be $6\sqrt 2$. If $y = 2x + c$ is a tangent to the hyperbola H, then the value of c² is equal to :