Find the equation of the straight lines passing through the point $(- 10, 4)$ and making an angle $θ$ with the line x-2y=10 ,such that tan $θ$ =2.

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Solution

So lines
$\begin{matrix} y - 4 = \frac{- 3}{4} (x - (- 10)) 4 (y - 4) = - 3 x - 30 3 x + 4 y + 14 = 0 \end{matrix}$
$\begin{matrix} a n d y - 4 = \infty (x - (- 10)) \frac{y - 4}{\infty} = x + 10 0 = x + 10 x + 10 = 0 \end{matrix}$

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Find the equation of the straight lines passing through the point (−10,4) and making an angle θ with the line x-2y=10 ,such that tan θ =2.

So linesy−4=−34(x−(−10))4(y−4)=−3x−303x+4y+14=0andy−4=∞(x−(−10))y−4∞=x+100=x+10x+10=0

Find the equation of the straight lines passing through the point $(- 10, 4)$ and making an angle $θ$ with the line x-2y=10 ,such that tan $θ$ =2.

So lines
$\begin{matrix} y - 4 = \frac{- 3}{4} (x - (- 10)) 4 (y - 4) = - 3 x - 30 3 x + 4 y + 14 = 0 \end{matrix}$
$\begin{matrix} a n d y - 4 = \infty (x - (- 10)) \frac{y - 4}{\infty} = x + 10 0 = x + 10 x + 10 = 0 \end{matrix}$