How will you find the vertex of a parabola given in 2nd degree form (the axis of parabola is not parallel to coordinate axes)?

show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)

show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0

A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius. 

 

Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d