1. TOPIC : CONE

2. DEFINITION OF CONE

3. HOMOGENEOUS EQUATION OF CONE

4. EQUATION OF CONE WITH VERTEX AT ORIGIN

6. EQUATION OF A CONE

7. EXAMPLES RELATED TO CONE

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

12. RIGHT CIRCULAR CONE

14. EQUATION OF RIGHT CIRCULAR CONE (STANDARD FORM)

20. EXAMPLES

23. 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.

24. EQUATION OF ENVELOPING CONE

26. ENVELOPIG CONE IN GENERAL FORM

27. EXAMPLES RELATED TO ENVELOPING CONE

33. INTERSECTION OF A STRAIGHT LINE AND A CONE

36. EQUATION OF THE TANGENT PLANE

39. ASSIGNMENT

40. 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

41. 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

42. 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).

43. TEST
NOTE: DO ANY TWO

44. 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).