What is the equation of the auxiliary circle of a hyperbola
$\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$

$x^{2} + y^{2} = 9$

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$x^{2} + y^{2} = 16$

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$x^{2} + y^{2} = 25$

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$x^{2} + y^{2} = 1$

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Solution

The correct option is B
$x^{2} + y^{2} = 16$

Auxiliary circle by definition is a circle which is concentric with the centre of the hyperbola and passes through the vertices of the hyperbola. Here vertices are (0, 4) and (0, -4)

Let's see how such a circle looks like in a diagram

∴ The required circle is

$x^{2} + y^{2} = 16$

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What the equation of the auxiliary circle of a hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$

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