TOPICTOPIC : : CONECONE

DEFINITION OF CONEDEFINITION OF CONE

HOMOGENEOUS EQUATION OF HOMOGENEOUS EQUATION OF CONECONE

EQUATION OF CONE WITH VERTEX EQUATION OF CONE WITH VERTEX AT ORIGINAT ORIGIN

EQUATION OF A CONEEQUATION OF A CONE

EXAMPLES RELATED TO CONEEXAMPLES RELATED TO CONE

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

RIGHT CIRCULAR RIGHT CIRCULAR CONECONE

EQUATION OF RIGHT EQUATION OF RIGHT CIRCULAR CONECIRCULAR CONE

(STANDARD FORM) (STANDARD FORM)

EXAMPLESEXAMPLES

ENVELOPING CONEENVELOPING CONE

The locus of tangent drawn from a The locus of tangent drawn from a fixedfixed

point to a sphere (or conicoid) is a point to a sphere (or conicoid) is a cone ,cone ,

called enveloping cone or tangent from called enveloping cone or tangent from

the point to the sphere.the point to the sphere.

EQUATION OF ENVELOPING EQUATION OF ENVELOPING CONECONE

ENVELOPIG CONE IN GENERAL ENVELOPIG CONE IN GENERAL FORMFORM

EXAMPLES EXAMPLES RELATED TO RELATED TO

ENVELOPING CONEENVELOPING CONE

INTERSECTION OF A STRAIGHT

LINE AND A CONE

EQUATION OF THE EQUATION OF THE TANGENT PLANETANGENT PLANE

ASSIGNMENTASSIGNMENT

Find the equation to the cone with Find the equation to the cone with vertex at the origin and which passes vertex at the origin and which passes through the curves xthrough the curves x22+y+y22=4,z=2=4,z=2

Find the equation to the cone with Find the equation to the cone with vertex at the origin and which passes vertex at the origin and which passes through thethrough the

intersection of the surfacesintersection of the surfaces 4x4x22+y+y22+z+z22+2x+4z=8+2x+4z=8 4x4x22+y+y22+z+z22+x+2z=4+x+2z=4

Find the equation of the cone whose Find the equation of the cone whose vertex is(vertex is(,,,,) and whose base is ) and whose base is

yy22=4ax,z=0=4ax,z=0 Find the equation of the cone whose Find the equation of the cone whose

vertex is(vertex is(,,,,) and whose base is) and whose base is axax22+by+by22=1,z=0=1,z=0 Find the equation of the cone whose Find the equation of the cone whose

vertex is the point (1,-1,2) and whose vertex is the point (1,-1,2) and whose guiding curve is 3xguiding curve is 3x22-y-y22=1,z=0=1,z=0

Find the equation to the right circular Find the equation to the right circular cone whose vertex is p(2,-3,5), axis pq cone whose vertex is p(2,-3,5), axis pq which makes equal angles with the co-which makes equal angles with the co-ordinates axis and semi-vertical angle is ordinates axis and semi-vertical angle is 3030..

Find the enveloping cone of the sphereFind the enveloping cone of the sphere xx22+y+y22+z+z22+2x-2y=2+2x-2y=2 with its vertex at (1,1,1)with its vertex at (1,1,1) Prove that Prove that 4x4x22-y-y22+2z+2z22+2xy-3yz+12x-+2xy-3yz+12x-

11y+6z+4=0 11y+6z+4=0 represent a cone whose vertex is (-1,-represent a cone whose vertex is (-1,-

2,-3). 2,-3).

TESTTEST

NOTE: DO ANY TWONOTE: DO ANY TWO

Find the equation to the cone,whose Find the equation to the cone,whose vertex is at the origin and which vertex is at the origin and which passes through the curves passes through the curves

xx22/4+y/4+y22/9+z/9+z22/1=1/1=1 x+y+z=1x+y+z=1 Find the equation of the conewith Find the equation of the conewith

vertex (1,1,1) and passes through the vertex (1,1,1) and passes through the curve of intersection of x+y+z=1 and curve of intersection of x+y+z=1 and xx22+y+y22+z+z22=1=1

Find the equation to the right circular Find the equation to the right circular cone, whose vertex is p(2,-3,5), axis pq cone, whose vertex is p(2,-3,5), axis pq which makes equal angles with the which makes equal angles with the axes and which passes through a(1,-axes and which passes through a(1,-2,3).2,3).