LESSON 1.0 - Introduction to Conic Sections.ppsx
- 1. Mr. Florben G. Mendoza INTRODUCTION TO CONIC SECTIONS
- 2. Mr. Florben G. Mendoza VERTEX AXIS BASE NAPPES GENERATOR LOWER UPPER DOUBLE RIGHT CIRCULAR CONE BASE Nappe - the curved lateral surface of the cone. Right circular cone - is a circular cone whose axis is perpendicular to the center of its base. Axis – is the fixed vertical line that passes through the vertex and the center of the base Vertex (apex) - the intersection of the axis and the generator. Vertex angle –the angle between the axis and the generator. Generator – the rotating line which runs from the vertex (apex) of the cone to the base. Base – is a flat circular surface whose center is perpendicular to the axis.
- 3. Mr. Florben G. Mendoza ELLIPSE PARABOLA CIRCLE HYPERBOLA CONIC SECTIONS are formed by the intersection of a right circular cone with a plane.
- 4. Mr. Florben G. Mendoza When a plane intersects the cone at an angle to the axis, in such a way that this angle is greater than the vertex angle, the conic section formed is an “ELLIPSE”. ELLIPSE a b b > a
- 5. Mr. Florben G. Mendoza When a plane intersects the cone parallel to the base and perpendicular to the axis, a “CIRCLE” is formed. CIRCLE perpendicular
- 6. Mr. Florben G. Mendoza When a plane intersects a cone such that the angle formed by the plane and the axis are equal to the vertex angle, the conic section formed is a “PARABOLA”. PARABOLA b = a b a
- 7. Mr. Florben G. Mendoza When the plane intersects both nappes and the angle between the plane and the axis is less than the vertex angle, a “HYPERBOLA” is formed. HYPERBOLA
- 8. Mr. Florben G. Mendoza DEGENERATE CONICS A degenerate conic is generated when a plane intersects the vertex of the cone.
- 9. Mr. Florben G. Mendoza DEGENERATE CONICS POINT ELLIPSE Point If the plane intersects the two cones at the vertex and at an angle greater than the vertex angle, we get a point. This is a degenerate ELLIPSE. a b b > a
- 10. Mr. Florben G. Mendoza DEGENERATE CONICS LINE PARABOLA LINE If the plane intersects the two cones at the vertex and at an angle equal to the vertex angle, we get a line. This is a degenerate PARABOLA.
- 11. Mr. Florben G. Mendoza DEGENERATE CONICS INTERSECTING HYPERBOLA LINES INTERSECTING LINES If the plane intersects the two cones at the vertex and at an angle less than the vertex angle, we get two intersecting lines. This is a degenerate HYPERBOLA.
- 12. Mr. Florben G. Mendoza