Find the equations of the straight lines which pass through $(3, 2)$ and make an angle of $45^{o}$ with the line $x = 2 y + 4$ .

Open in App

Solution

$tan θ = ∣ ∣ ∣ \frac{m_{2} - m_{1}}{1 - m_{2} m_{1}} ∣ ∣ ∣$

$x = 2 y + 4$

$\Rightarrow y = \frac{x}{2} - 2$

$\Rightarrow m_{1} = \frac{1}{2}$

$1 = ∣ ∣ ∣ ∣ ∣ \frac{m_{2} - \frac{1}{2}}{1 - m_{2} \frac{1}{2}} ∣ ∣ ∣ ∣ ∣$

$∴ \frac{m_{2} - \frac{1}{2}}{1 - m_{2} \frac{1}{2}} = \pm 1$

Solving for $m_{2}$ we get,

$m_{2} = 2, \frac{- 1}{2}$

$(y - y_{1}) = m (x - x_{1})$

$(y - 2) = 2 (x - 3)$ $(y - 2) = \frac{- 1}{2} (x - 3)$

$y - 2 = 2 x - 6$ $2 y - 4 = x - 3$

$y - 2 x + 4 = 0$ $2 y - x + 1 = 0$

Hence required equations of line are $y - 2 x + 4 = 0$ or $2 y - x + 1 = 0$

Suggest Corrections

Similar questions

45^{o}

\sqrt{3} x + y = 11

(3, 2)

45^{\circ}

x - 2 y = 3

Find the equations of the lines through the point (3, 2), which make an angle of $45^{\circ}$ with the line $x - 2 y = 3$

(- 3, 2)

45^{t h}

3 x - y + 4 = 0

(3, 2)

45^{\circ}

x - 2 y = 3

Join BYJU'S Learning Program