Question

( frac{1+sqrt{3}}{1-sqrt{3}}=frac{m_{1}-m_{2}}{1+m_{1} m} )
Prurs
( Rightarrow quad 1 quad=quad m_{1}-m )
( 2 n )
1) for a line having slope ( m_{1} ) and othere lein having Slope ( m_{2} ), the acute ongle between
( Rightarrow quad m_{1} m_{2}+1=m_{1}^{2}-m_{1} m_{2} )
(2) for a luin having ( 2 M y )
( =-frac{9}{b} )
(3) Point slobe equater of buic in ( m_{L}=1-sqrt{3} quad-1(1+sqrt{3}) )
Slope equatuin of luil in ( y-y_{1}=mleft(x-x_{1}right) quad ) i foint ( left(x_{1}+x_{1}right) )
( m_{2}=1+3-2 sqrt{3}-(1+3+2 sqrt{3} )
(1) Sbe of luie ( x+y+sqrt{3}(y-x)-a=0 quad 2(1+sqrt{3})(1-sqrt{3}) )
( =(sqrt{3}+1) y+(sqrt{3}-1) x-a=0 )
( Rightarrow(sqrt{3}-1) x+(sqrt{3}+1) y-a=0 )
( m_{1}=frac{-(sqrt{3}-1)}{sqrt{3}+1}=frac{1-sqrt{3}}{1+sqrt{3}} )
(2) Whe slope of Required luic is ( m_{2} ) ( m_{2}=-4 sqrt{3} )
begin{tabular}{l|l|lllll}
hline ( operatorname{an}(80+45) ) & ( = ) & ( m_{1}-m_{2} ) & & &
hline & ( 1+m_{1} m_{2} ) & & & & &
hline
end{tabular}
( frac{sqrt{3}+1}{frac{1}{sqrt{3}}-1}=frac{m_{1}-m_{2}}{1+m_{1} m_{2}} )
( -0=sqrt{3}(x-0) )
( =sqrt{3} x )

# 19. Find the equations to the straight lines which pass through origin and are inclined at 75° to the straight line x + y + 3(y - x) = a

Solution