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TOPIC : CONE

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.

graiden-frederick
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TOPIC : CONE

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  1. TOPIC : CONE

  2. DEFINITION OF CONE

  3. HOMOGENEOUS EQUATION OF CONE

  4. EQUATION OF CONE WITH VERTEX AT ORIGIN

  5. EQUATION OF A CONE

  6. EXAMPLES RELATED TO CONE

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

  8. RIGHT CIRCULAR CONE

  9. EQUATION OF RIGHT CIRCULAR CONE (STANDARD FORM)

  10. EXAMPLES

  11. 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.

  12. EQUATION OF ENVELOPING CONE

  13. ENVELOPIG CONE IN GENERAL FORM

  14. EXAMPLES RELATED TO ENVELOPING CONE

  15. INTERSECTION OF A STRAIGHTLINE AND A CONE

  16. EQUATION OF THE TANGENT PLANE

  17. ASSIGNMENT

  18. 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

  19. Find the equation of the cone whose vertex is(,,) and whose base is y2=4ax,z=0 • Find the equation of the cone whose vertex is(,,) and whose base is 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

  20. 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).

  21. TEST • NOTE: DO ANY TWO

  22. 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).

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