Find the equation of the straight line,which passes through the point (2,3) and making of an angle of 45 degree - Maths - Vector Algebra

Question

Find the equation of the straight line,which passes through the
point (2,3) and making of an angle of 45 degree with the line
x-3y=2

Priyanka Kedia · Accepted Answer

The equation of the straight line which passes through the point 2,3 isy-3=mx-2             
1where m is slope of the equation
Slope of given line x-3y=2⇒y=-13x+23 is as,m1=-13Since angle between the two line is 450
 Therefore,tan 450=m+131-m×13⇒1=3m+13-m
⇒3m+13-m=±1⇒3m+1=±3-mTaking +ve sign:3m+1=3-m⇒m=12Substitute value of m=12 in equation 1,y-3=12x-2⇒2y-6=x-2⇒x-2y+4=0
Taking -ve sign:3m+1=-3+m⇒m=-2Substitute value of m=-2 in equation 1,y-3=-2x-2⇒y-3=-2x+4⇒2x+y-7=0

Find the equation of the straight line,which passes through the point (2,3) and making of an angle of 45 degree with the line x-3y=2