TOPIC : CONE

DEFINITION OF CONE

HOMOGENEOUS EQUATION OF CONE

EQUATION OF CONE WITH VERTEX AT ORIGIN

EQUATION OF A CONE

EXAMPLES RELATED TO CONE

EQUATION OF CONE WITH A GIVEN VERTEX AND BASE A GIVEN CONIC

RIGHT CIRCULAR CONE

EQUATION OF RIGHT CIRCULAR CONE (STANDARD FORM)

EXAMPLES

ENVELOPING CONE The locus of tangent drawn from a fixed point to a sphere (or conicoid) is a cone , called enveloping cone or tangent from the point to the sphere.

EQUATION OF ENVELOPING CONE

ENVELOPIG CONE IN GENERAL FORM

EXAMPLES RELATED TO ENVELOPING CONE

INTERSECTION OF A STRAIGHT LINE AND A CONE

EQUATION OF THE TANGENT PLANE

ASSIGNMENT

Find the equation to the cone with vertex at the origin and which passes through the curves x2+y2=4,z=2 Find the equation to the cone with vertex at the origin and which passes through the intersection of the surfaces 4x2+y2+z2+2x+4z=8 4x2+y2+z2+x+2z=4

Find the equation of the cone whose vertex is(,,) and whose base is y2=4ax,z=0 ax2+by2=1,z=0 Find the equation of the cone whose vertex is the point (1,-1,2) and whose guiding curve is 3x2-y2=1,z=0

Find the equation to the right circular cone whose vertex is p(2,-3,5), axis pq which makes equal angles with the co-ordinates axis and semi-vertical angle is 30. Find the enveloping cone of the sphere x2+y2+z2+2x-2y=2 with its vertex at (1,1,1) Prove that 4x2-y2+2z2+2xy-3yz+12x-11y+6z+4=0 represent a cone whose vertex is (-1,-2,-3).

TEST NOTE: DO ANY TWO

Find the equation to the cone,whose vertex is at the origin and which passes through the curves x2/4+y2/9+z2/1=1 x+y+z=1 Find the equation of the conewith vertex (1,1,1) and passes through the curve of intersection of x+y+z=1 and x2+y2+z2=1 Find the equation to the right circular cone, whose vertex is p(2,-3,5), axis pq which makes equal angles with the axes and which passes through a(1,-2,3).