Q. The equation of the lines through the point (3, 2) which makes an angle of $45{^\circ}$ with the line $x - 2y = 3$ , are
A) $3x - y = 7$ and $x + 3y = 9$
B) $x - 3y = 7\$ and $3x + y = 9$
C) $x - y = 3$ and $x + y = 2$
D) $2x + y = 7$ and $x - 2y = 9$
Explanation
(a)
The slope of line $x - 2y = 3is\ \frac{1}{2}$
Let the slope of required lines is $m$
$\therefore\tan{45{^\circ}} = \pm \left| \frac{\frac{1}{2} - m}{1 + \frac{m}{2}} \right|$
$\Rightarrow 1 + \frac{m}{2} = \pm \left( \frac{1}{2} - m \right) \Rightarrow m = - \frac{1}{3},3$
$\therefore\$Equation of line with slope $m = - \frac{1}{3}$ and passing through (3, 2), is
$(y - 2) = - \frac{1}{3}(x - 3)\ \Rightarrow \ x + 3y = 9$
and another equation of line with slope $m = 3$and passing through (3, 2) is
$(y - 2) = 3(x - 3)\ \Rightarrow \ 3x - y = 7$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.