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  • The equations of the lines through the point (3,2) and the line makes an angle 45° with the line x – 2y = 3 isOption: 1 2x - y = 4

The equations of the lines through the point (3,2) and the line makes an angle 45° with the line x – 2y = 3 is

Option: 1

2x - y = 4


Option: 2

x - 2y + 1 = 0


Option: 3

x - 2y - 1 = 0


Option: 4

3x - y = 7


Answers (1)

best_answer

Slope of the given line is m1 = 1/2

Let the slope of the required line be 'm'

Then,

\\\tan \left(45^{\circ}\right)=\left|\frac{m-\frac{1}{2}}{1+\frac{m}{2}}\right|\\ {\Rightarrow\left|\frac{2 m-1}{2+m}\right|=1} \\ {\Rightarrow \quad \frac{2 m-1}{2+m}=1 \text { or } \frac{2 m-1}{2+m}=-1} \\ {\Rightarrow \quad m=3 \text { or } m=-\frac{1}{3}}

Hence, the equation of the lines are

\\ {y-2=3(x-3) \text { and } y-2=-\frac{1}{3}(x-3)} \\ {\Rightarrow \quad 3 x-y-7=0 \text { and } x+3 y-9=0}

Posted by

Irshad Anwar

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