Cone

Author Bhawna asked on 2019-07-22 13:26:00

The equation of the cone is

x2+2y2-3z2-2yz+5zx+3xy=o (given)

its vertex  is ( 0,0,0) and it is homogenous equation x,y,z

the equation of the generator  of the cone  with direction  ( 1,1,-1) are

x-0/1= y-0/1= z-0/-1

Any point on the generator is  (r,r,-r)

The equation ate point P will be

 x(r)+2y(r)-3z(-r)-[y(-r) +z(r)]+5/2[z(r)+x(-r)]+3/2[x(r)+y(r)]=0

after solving we will get

    y+z=0

The equation of the cone is

x2+2y2-3z2-2yz+5zx+3xy=-0

its vertex  is ( 0,0,0) and it is homogenous equation x,y,z

the equation of the generator  of the cone  with direction  ( 1,1,-1) are

x-0/1= y-0/1= z-0/-1

Any point on the generator is  (r,r,-r)

The equation ate point P will be

 x(r)+2y(r)-3z(-r)-[y(-r) +z(r)]+5/2[z(r)+x(-r)]+3/2[x(r)+y(r)]=0

after solving we will get

    y+z=0