The equation of the lines through the point (3,2) which makes an angle of 45^ with the line x-2 y=3 are

Step-by-step solution

Let m₁ be the slope of the line, which passes through the point (3,2) and m₂ be the slope of x-2 y=3 m₂= - Coefficient of x Coefficient of y m₂= -1 -2 m₂= 1 2 Given that, the angle between lines is 45^ 45^ = | m₁-m₂ 1+m₁ m₂ |1= | m₁- 1 2 1+m₁ ( 1 2 ) | When, 1=+ ( 2 m₁-1 2+m₁ ) aligned & & 2+m₁ & =2 m₁-1 & & m₁ & =3 aligned and when 1=- ( 2 m₁-1 2+m₁ ) m₁= -1 3 Hence, equation a line passing through (3,2) and having slope 3 is