AP EAMCET · Maths · Straight Lines
If the straight line passing through \(P(3,4)\) makes an angle \(\frac{\pi}{6}\) with the positive \(x\)-axis in anticlockwise direction and meets the line \(12 x+5 y+10=0\) at Q , then the length of the segment PQ is
- A \(\frac{64}{12 \sqrt{2} 1}\)
- B \(\frac{96}{9 \sqrt{2}-1}\)
- C \(\frac{112}{10 \sqrt{3}+3}\)
- D \(\frac{132}{12 \sqrt{3}+5}\)
Answer & Solution
Correct Answer
(D) \(\frac{132}{12 \sqrt{3}+5}\)
Step-by-step Solution
Detailed explanation
Any line through \(P(3,4)\) making an angle with \(x\)-axis is \(\frac{x-3}{\cos 30^{\circ}}=\frac{y-4}{\sin 30^{\circ}}=r\) Any point \(Q\) on it is \(\left(\frac{r \sqrt{3}}{2}+3, \frac{r}{2}+4\right)\) and \(Q\) lies on \(12 x+5 y+10=0\)…
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