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Director circle and auxiliary circle of a hyperbola - class-XI
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For the hyperbola $\dfrac{x^2}{64}-\dfrac{y^2}{36}=1$, the equation of director circle is
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A
$x^2+y^2=28$
💡 Explanation:
The Director circle of a hyperbola is defined as the locus of the point of intersection of two perpendicular tangents to the hyperbola. For any standard hyperbola $\dfrac{x^2}{a^2} -\dfrac {y^2}{b^2} = 1$,
The equation of Director circle is given by $x^2 + y^2 = a^2 - b^2$
Here the given hyperbola is $\dfrac{x^2}{64} -\dfrac {y^2}{36} = 1$,
Here $a =8$ and $b =6$
So equation of the director circle will be $x^2 + y^2 = (8)^2 - (6)^2$
$\Rightarrow x^2 + y^2 = 28$
Correct option is $C$.