If the lines represented by $4 x^{2} + 12 x y + 9 y^{2} - 6 x - 9 y$ = 1 are 2 tangents to a circle then its area is

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11/14

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Solution

The correct option is D
11/14

$4 x^{2} + 12 x y + 9 y^{2} - 6 x - 9 y$ = 1

Pair of parallel lines

Distance = $2 \sqrt{\frac{9 + 4}{4 (4 + 9)}}$ = $2 \times \frac{1}{2}$ = 1

Radius = $\frac{1}{2}$

Area = $π r^{2}$ = $\frac{2211}{7} \times \frac{1}{42}$ = $\frac{11}{14}$

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