If a circle of radius 4 cm passes through the foci of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1$ and concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is

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Aicharya · Accepted Answer

Given that circle passes through foci of given hyperbola and have radius 4 .

$\therefore \quad c=4$ and $b=2$ [ from equation of hyperbola] $\because \quad a^2+b^2=c^2 \Rightarrow a^2+4=16 \Rightarrow a=2 \sqrt{3}$ For congugate hyperbola $a=2$ and $c=4$ $\therefore c=a e=4 \Rightarrow 2 e=4 \Rightarrow e=2$

If a circle of radius 4 cm passes through the foci of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1$ and…

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