THREE DIMENSIONAL GEOMETRY
Definition, Equation of a sphere, General equation of a sphere, Centre and radius of a sphere, Great circle, Equation of circle, Diameter form of the equation of a sphere, Tangent line and tangent plane of a sphere, Condition of tangency for a line and tangent plane, Angle of intersection of two spheres, Condition of orthogonality of two spheres.
Condition for general equation of second degree to represent various form of surfaces, Cone, Quadratic cone, Enveloping cone, Condition for general equation of second degree to represent a cone, Intersection with a line and a plane, Angle between the intersecting lines of cone, Tangent plane.
Reciprocal cone, Right circular cone, Definition and equation of a cylinder, Enveloping cylinder, Right circular cylinder.
Conicoid, Central conicoid, Standard equation of ellipsoid, hyperboloid of one sheet and hyperboloid of two sheets, Nature and shape of central conicoid, Intersection of a line and a central conicoid, Tangent line and tangent plane, Condition of tangency, Director sphere.
Developable surface, Skew surface, Generating lines of central conicoid, System of generating lines, Equation of generator through one point and two points on the principle elliptic section of a hyperboloid of one sheet.
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- P R Vittal, Analytical Geometry: 2D and 3D, Pearson Education India, 2013.
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