The joint equation of two lines through the origin, each of which making an angle of 30^ with line x+y=0 is

Step-by-step solution

Given equation of line is x+y=0 , having slope =-1 (1) Required line makes angle of 30^ with given line (1) 30^ = | m+1 1-m | 1 3 = | m+1 1-m | On squaring both sides, we get array l 1 3 = (m+1)² (1-m)² (1-m)²=3(m+1)² 1-2 m+m²=3 (m²+2 m+1 ) 3 m²+6 m+3-1+2 m-m²=0 2 m²+8 m+2=0 m²+4 m+1=0 array aligned Put m =& y x & y ² x ² + 4 y x +1=0 y ²+4 xy + x ²=0 aligned