Find-the-equation-of-the-line-through-2-3-which-make-angles-45-with-the-line-2x-y-2-

Question Number 38879 by Rio Mike last updated on 30/Jun/18

F i n d t h e e q u a t i o n o f t h e l i n e t h r o u g h

(2, - 3) w h i c h m a k e a n g l e s 45 ° w i t h

t h e l i n e 2 x - y = 2 .

Answered by MrW3 last updated on 30/Jun/18

l i n e 2 x - y = 2 :

\tan θ = m = 2

k = \tan (θ \pm \frac{π}{4}) = \frac{\tan θ \pm \tan \frac{π}{4}}{1 \mp \tan θ \tan \frac{π}{4}} = \frac{m \pm 1}{1 \mp m}

= \frac{2 \pm 1}{1 \mp 2} = {\begin{cases} - 3 \\ \frac{1}{3} \end{cases}

\Rightarrow e q n . o f n e w l i n e :

\frac{y + 3}{x - 2} = - 3 o r \frac{1}{3}

\Rightarrow y + 3 = - 3 (x - 2)

\Rightarrow 3 x + y = 3

o r

\Rightarrow 3 (y + 3) = x - 2

\Rightarrow x - 3 y = 11

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