Question

find the separate equation of the pair of straight lines represented by (x^2+y^2)sina.cosa+xy=0​

Answer 1

Let equation of the lines given by x2+2hxy+y2=0 bey=m1x andy=m2x.

Since these lines make an angel a with y+x=0 whose slope is −1.

∴1−m1m1+1=tana=1−m2−1−m2

⇒m1=tana+1tana−1 and m2=tana−1tana+1 

⇒m1+m2=tan2a−1(tana−1)2+(tana+1)2

=cos2a2sec2a×cos2a