topic : cone
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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TOPICTOPIC : : CONECONE
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DEFINITION OF CONEDEFINITION OF CONE
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HOMOGENEOUS EQUATION OF HOMOGENEOUS EQUATION OF CONECONE
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EQUATION OF CONE WITH VERTEX EQUATION OF CONE WITH VERTEX AT ORIGINAT ORIGIN
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EQUATION OF A CONEEQUATION OF A CONE
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EXAMPLES RELATED TO CONEEXAMPLES RELATED TO CONE
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EQUATION OF CONE WITH A GIVEN VERTEX AND EQUATION OF CONE WITH A GIVEN VERTEX AND BASE A GIVEN CONICBASE A GIVEN CONIC
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RIGHT CIRCULAR RIGHT CIRCULAR CONECONE
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EQUATION OF RIGHT EQUATION OF RIGHT CIRCULAR CONECIRCULAR CONE
(STANDARD FORM) (STANDARD FORM)
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EXAMPLESEXAMPLES
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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.
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EQUATION OF ENVELOPING EQUATION OF ENVELOPING CONECONE
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ENVELOPIG CONE IN GENERAL ENVELOPIG CONE IN GENERAL FORMFORM
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EXAMPLES EXAMPLES RELATED TO RELATED TO
ENVELOPING CONEENVELOPING CONE
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INTERSECTION OF A STRAIGHT
LINE AND A CONE
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EQUATION OF THE EQUATION OF THE TANGENT PLANETANGENT PLANE
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ASSIGNMENTASSIGNMENT
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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
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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
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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).
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TESTTEST
NOTE: DO ANY TWONOTE: DO ANY TWO
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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).