Prove that the equations:

Q1y^2(cosa+sina)cosa - xy( sin2a - cos2a) +x^2( sina - cosa)sina=0 representsstraight line inclined at 60 to each other .

Prove also that the area of the triangle formed with them by the straight line (cosa -sina)y -(sina+cosa) x +b=0

is b^2/(4)

Q2. Show that the pair

ax^2 +2hxy +by^2 +( x^2 +y^2) =0 is equally inclined to the same pair.

Q.3. The vertices of triangle lie on y=xtana,y=xtanb,y=xtanc the circumcenter being origin .prove the locus of intersection of the ortho centre is the line x(sina+sinb+sinc)= y(cosa+cosb+cosc)

Q4. The base of the triangle passes through (f,g) and the sides are bisected at right angles by x+y=0,y=9x.find the locus of the vertex