The locus of the centre of a circle touching the lines $2 x + 3 y - 2 = 0 and 2 x - 3 y + 2 = 0$ may be

x = 0

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y = \frac{2}{3}

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3 x y + 2 x = 0

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3 x y - 2 x = 0

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Solution

The correct option is D $3 x y - 2 x = 0$
Centre will lie on the angle bisector of tangents
and which is given by

$\frac{2 x + 3 y - 2}{\sqrt{13}} = \pm \frac{2 x - 3 y + 2}{\sqrt{13}}$

$\Rightarrow x = 0, y = \frac{2}{3} or 3 x y - 2 x = 0$

Suggest Corrections

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