Find the equation of the lines through the point (3, 2) which make an angle of `45^@`with the line `x-2y=3`.

Explanation

Let the slope of the required line be m1​.

The given line can be written as `y=1/2​x−3/2`​, which is of the form y=mx+c

∴ slope of the given line =m2​=`1/2`

It is given that the angle between the required line and line x−2y=3 is 45∘

We know that if θ is the acute angle between lines `l_1`​ and `l_2`​ with slopes `m_1`​ and `m_2`​ respectively, then `tanθ=(m_2-m_1)/(1+m_1m_2)`

∴`tan45∘=(m_2-m_1)/(1+m_1m_2)`

⇒`1=|(1/2-m_1)/(1+m_1/2)|`


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