The equation of one of the straight lines which passes through the point (1, 3) and makes …

Question

The equation of one of the straight lines which passes through the point (1, 3) and makes an angles $${\tan ^{ - 1}}\left( {\sqrt 2 } \right)$$ with the straight line, y + 1 = 3$${\sqrt 2 }$$ x is :

Accepted Answer

Let slope of line be m

$$ \therefore $$ $$\left| {{{m - 3\sqrt 2 } \over {1 + 3\sqrt 2 m}}} \right| = \sqrt 2 $$

$$ \Rightarrow m - 3\sqrt 2  =  \pm \,\sqrt 2  \pm 6m$$

$$ \Rightarrow m \mp 6m =  \pm \sqrt 2  + 3\sqrt 2 $$

$$ \Rightarrow m =  - {{4\sqrt 2 } \over 5}$$ or $${{2\sqrt 2 } \over 7}$$

Hence line can be

$$y - 3 = {{ - 4\sqrt 2 } \over 5}(x - 1)$$

$$ \Rightarrow 5y - 15 =  - 4\sqrt 2 x + 4\sqrt 2 $$

$$ \Rightarrow 4\sqrt 2 x + 5y - (15 + 4\sqrt 2 ) = 0$$

Solutions · 1