Find the equation of the line through (2,−3) which make angles 45° with the line 2x − y = 2.


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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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