If a straight line passing through the point P(3, 4) and makes an angle π6with the x – axis and meets the line 12x+5y+10=0 at Q then the length of PQ is

PQ=ax1+by1+cacosα+bsinα=132123+5

If a straight line passing through the point P(3, 4) and makes an angle π6with the x – axis and meets the line 12x+5y+10=0 at Q then the length of PQ is

PQ=ax1+by1+cacosα+bsinα=132123+5

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If a straight line passing through the point P(3, 4) and makes an angle $\frac{π}{6}$ with the x – axis and meets the line $12 x + 5 y + 10 = 0$ at Q then the length of PQ is

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$\frac{132}{12 \sqrt{3} + 5}$

$\frac{66}{8 \sqrt{3} + 6}$

$\frac{182}{6 \sqrt{3} + 4}$

$\frac{192}{14 \sqrt{3} + 6}$

answer is A.

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$P Q = |\frac{a x_{1} + b y_{1} + c}{a \cos α + b \sin α}| = \frac{132}{12 \sqrt{3} + 5}$

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If a straight line passing through the point P(3, 4) and makes an angle π6with the x – axis and meets the line 12x+5y+10=0 at Q then the length of PQ is

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If a straight line passing through the point P(3, 4) and makes an angle $\frac{π}{6}$ with the x – axis and meets the line $12 x + 5 y + 10 = 0$ at Q then the length of PQ is