Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is

Engineering

Mathematics

Various Form of a Straight Line

Question

$\frac{1 - \sqrt{7}}{1 + \sqrt{7}}$

$\frac{\sqrt{5} - 1}{\sqrt{5} + 1}$

$\frac{\sqrt{7} - 1}{\sqrt{7} + 1}$

$\frac{1 - \sqrt{5}}{1 + \sqrt{5}}$

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

x = 2 + r cosθ

y = 3 + r sinθ

⇒ 2 + r cosθ + 3 + r sinθ = 7

⇒ r (cosq + sinq) = 2

$\Rightarrow sinθ + cosθ = \frac{2}{r} = \frac{2}{\pm 4} = \pm \frac{1}{2}$

$\Rightarrow 1 + sinθ = \frac{1}{4}$

$\Rightarrow \sin 2 θ = - \frac{3}{4}$

$\Rightarrow \frac{2 m}{1 + m^{2}} = - \frac{3}{4}$

⇒ 3m² + 8m + 3 = 0

$\Rightarrow m = \frac{- 4 \pm \sqrt{7}}{1 - 7}$

$\frac{1 - \sqrt{7}}{1 + \sqrt{7}} = \frac{{(1 - \sqrt{7})}^{2}}{1 - 7} = \frac{8 - 2 \sqrt{7}}{- 6} = \frac{- 4 + \sqrt{7}}{3}$