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Question Number 55071 by peter frank last updated on 17/Feb/19

	Answered by mr W last updated on 17/Feb/19

	$t h e l i n e t h r o u g h o r i g i n a n d p e r p e n d i c u l a r t o$ $l i n e l x + m y + n = 0 i s :$ $m x - l y = 0 o r y = \frac{m}{l} x$ $l e t \tan θ_{0} = \frac{m}{l}$ $l i n e 1 i s y = \tan θ_{1} x w i t h θ_{1} = θ_{0} - \frac{π}{4}$ $l i n e 2 i s y = \tan θ_{2} x w i t h θ_{2} = θ_{0} + \frac{π}{4}$ $\tan θ_{1} = \frac{\frac{m}{l} - 1}{1 + \frac{m}{l}} = \frac{m - l}{m + l}$ $\tan θ_{2} = \frac{\frac{m}{l} + 1}{1 - \frac{m}{l}} = \frac{m + l}{l - m}$ $l i n e 1 :$ $y = \frac{m - l}{m + l} x o r (l - m) x + (l + m) y = 0$ $l i n e 2 :$ $y = \frac{m + l}{l - m} x o r (l + m) x + (m - l) y = 0$
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