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6.5. Transition from the general equation of a line to normal . . . . . . 48
6.6. Distance from the point to the line . . . . . . . . . . . . . . . 49
6.7. The angle between two lines on a plane . . . . . . . . . . . . . 50
Lecture 7. Lines of the second order . . . . . . . . . . . . . . . . . . . . 51
7.1. Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7.2. Ellipse . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
7.3. Hyperbola . . . . . . . . . . . . . . . . . . . . . . . . . 55
7.4. Parabola . . . . . . . . . . . . . . . . . . . . . . . . . . 60
7.5. Reducing the general equation of a line of the second order to the
canonical view . . . . . . . . . . . . . . . . . . . . . . . . . 62
Lecture 8. Analytic geometry in space . . . . . . . . . . . . . . . . . . . 64
8.1. Equation of surface and line in space . . . . . . . . . . . . . . 64
8.2. Equations of the plane. . . . . . . . . . . . . . . . . . . . . 65
8.2.1. Equation of a plane, which passes through a fixed point and is perpen-
dicular to the given vector. . . . . . . . . . . . . . . . . . . . . 65
8.2.2. General equation of a plane. . . . . . . . . . . . . . . . . . 66
8.2.3. Equation of a plane passing through three given points . . . . . . 66
8.2.4. Equation of a plane in segments . . . . . . . . . . . . . . . . 67
8.2.5. Normal equation of a plane . . . . . . . . . . . . . . . . . . 68
8.3. Change from a general equation of a plane to the normal one . . . . 69
8.4. Distance from the point to a plane . . . . . . . . . . . . . . . 69
8.5. Angle between two planes. . . . . . . . . . . . . . . . . . . 70
8.6. Equations of the straight line in space . . . . . . . . . . . . . . 71
8.6.1. Canonical equation of a line. . . . . . . . . . . . . . . . . . 72
8.6.2. Equation of a line passing through two points . . . . . . . . . . 73
8.6.3. Vector equation of a line. Parametric equation of a line . . . . . . 73
8.7. Distance from a point to a line in space . . . . . . . . . . . . . 74
8.8. Angle between two lines in space . . . . . . . . . . . . . . . 75
8.9. Mutual location of a line and a plane . . . . . . . . . . . . . . . 75
8.9.1. Angle between a line and a plane . . . . . . . . . . . . . . . 75
8.9.2. Conditions of parallelity and perpendicularity of a line and a plane . 76
8.10. Point of crossing point of a line with a plane . . . . . . . . . . . 77
Lecture 9. Surfaces of the second order . . . . . . . . . . . . . . . . . . 78
9.1. Canonical equations of surfaces of the second order. Method of parallel
cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
9.2. Ellipsoid. Sphere . . . . . . . . . . . . . . . . . . . . . . 78
9.3. One-sheet hyperboloid . . . . . . . . . . . . . . . . . . . . 78
9.4. Two-sheet hyperboloid . . . . . . . . . . . . . . . . . . . . 80
9.5. Elliptic paraboloid . . . . . . . . . . . . . . . . . . . . . . 81
9.6. Hyperbolic paraboloid . . . . . . . . . . . . . . . . . . . . 82
9.7. Cone of the second order . . . . . . . . . . . . . . . . . . . 83
9.8. Equation of a cylinder surface . . . . . . . . . . . . . . . . . 84
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
References . . . . . . . . . . . . . . . . . . . . . . . . . . 89

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