If a straight line through the point P(3, 5) makes an angle $\frac{π}{6}$ with +ve x-axis and meets the lines $2 x + y + 5 = 0$ $& 3 x - 2 y + 7 = 0$ at Q & R then $\frac{P Q}{P R} =$

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$\frac{3 \sqrt{3} - 2}{2 \sqrt{3} + 1}$

$\frac{(6 \sqrt{3} + 3)}{(12 \sqrt{3} - 8)}$

$\frac{2 (12 \sqrt{3} - 8)}{6 \sqrt{3} + 3}$

$\frac{3 \sqrt{3} + 1}{3 \sqrt{3} - 2}$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Here line is $\frac{x - 3}{\sqrt{3} / 2} = \frac{y - 5}{1 / 2} = r (let)$

$∴ Q (3 + \frac{\sqrt{3} r_{1}}{2}, 5 + \frac{r_{1}}{2}), R (3 + \frac{r_{1} \sqrt{3}}{2}, 5 + \frac{r_{2}}{2})$

$∴ 2 (3 + \frac{\sqrt{3} r_{1}}{2}) + 5 + \frac{r_{1}}{2} + 5 = 0$ and $3 (3 + \frac{r_{2} \sqrt{3}}{2}) - 2 (5 + \frac{r_{1}}{2}) + 7 = 0$

$\Rightarrow r_{1} = \frac{- 32}{2 \sqrt{3} + 1} & r_{2} = \frac{- 12}{3 \sqrt{3} - 2}$

$∴ \frac{P Q}{P R} = \frac{24 \sqrt{3} - 16}{6 \sqrt{3} + 3}$

Watch 3-min video & get full concept clarity