TS EAMCET · Maths · Straight Lines
If the straight line passing through the point \(P(3,4)\) makes an angle \(\frac{\pi}{6}\) with the positive direction of \(X\)-axis and meets the line \(12 x+5 y+10=0\) at \(Q\), then the length of \(P Q\) is
- A \(\frac{44}{12 \sqrt{2}+9}\)
- B \(\frac{66}{12 \sqrt{3}+5}\)
- C \(\frac{132}{12 \sqrt{3}+5}\)
- D \(\frac{148}{6 \sqrt{2}+3}\)
Answer & Solution
Correct Answer
(C) \(\frac{132}{12 \sqrt{3}+5}\)
Step-by-step Solution
Detailed explanation
(c) The equation of line passes through point \(P(3,4)\) makes an angle \(\frac{\pi}{6}\) with the positive direction of \(X\)-axis is \(\frac{x-3}{\cos \frac{\pi}{6}}=\frac{y-4}{\sin \frac{\pi}{6}}=r\) So, let point \(Q\left(3+\frac{\sqrt{3} r}{2}, 4+\frac{r}{2}\right)\),…
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