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Chord of Contact: Hyperbola

The circle ...

Question

The circle $4 x^{2} + 4 y^{2} - 12 x - 12 y + 9 = 0$

touches both the axes

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touches both the x-axis only

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touches both the y-axis only

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does not touch the axes

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Solution

The correct option is A touches both the axes
$4 x^{2} + 4 y^{2} - 12 x - 12 y + 9 = 0$
$\Rightarrow x^{2} + y^{2} - 3 x - 3 y + \frac{9}{4} = 0$
Center is $(\frac{3}{2}, \frac{3}{2})$ and radius $= \sqrt{\frac{9}{4} + \frac{9}{4} - \frac{9}{4}} = \frac{3}{2}$
Hence given circle touches both the axes.

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