A tangent is drawn at any point P(t) on parabola y² =8x where P(t) :x-coordinate = 2t² , y-coordinate = 4t . On this tangent, a point Q(a,b) is taken, from which pair of tangents QA and QB are drawn to circle x² + y² = 4.

(1) Find equation of locus of point of concurrency of chord of contact AB of the circle.

(2) Find equation of locus of circumcentre of triangle AQB if t = 2.

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