Lecture #6 analytic geometry
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The document discusses parabolas including their parts, graphs, and equations. It defines a parabola as the locus of points where the distance to the focus is equal to the distance to the directrix. The parts of a parabola include the vertex, focus, directrix, axis of symmetry, and latus rectum. The document outlines the graphs of parabolas with the vertex at the origin or at a point (h,k), and opening in different directions. It notes equations will be provided for parabolas with the vertex at the origin or (h,k), but does not show the actual equations.
Lecture #6 analytic geometry
- 1. Lecture #6 • Parabola • Parts of Parabola • Equations of Parabola with center at origin • Equations of parabola with center at (h, k) • Graph of Parabola
- 2. PARABOLA Locus of points such that the distance from a point to the focus is equal to the distance from the same point and the directrix.
- 3. PARTS OF PARABOLA Vertex – sharpest turn point of the parabola. (represented by V) Focus – a point which is used to determine or define the parabola. (represented by F) Latus Rectum – a line passing through the focus, perpendicular to the axis of symmetry, and it has two endpoints. Directrix – a line perpendicular to axis of symmetry (represented by D) Axis of symmetry – a line that divides the parabola in half Eccentricity – the eccentricity of the parabola is always equal to one. (represented by e)
- 5. GRAPHS OF PARABOLA The graph of parabola if the vertex is at the origin, and opens to the right,
- 6. The graph of parabola if the vertex is at the origin, and opens to the left,
- 7. The graph of parabola if the vertex is at the origin, and opens upward,
- 8. The graph of parabola if the vertex is at the origin, and opens downward,
- 9. The graph of parabola if the vertex is at (h, k) , and opens to the right,
- 10. The graph of parabola if the vertex is at (h, k) , and opens to the left,
- 11. The graph of parabola if the vertex is at (h, k) , and opens upward,
- 12. The graph of parabola if the vertex is at (h, k) , and opens downward,
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- 22. FORMULAS VERTEX AT (0, 0 ) FOCUS DIRECTRIX ENDS OF LATUS RECTUM LENGTH OF LATUS RECTUM EQUATION OF PARABOLA RIGHT LEFT UPWARD DOWNWARD
- 23. FORMULAS VERTEX AT (h, k) FOCUS DIRECTRIX ENDS OF LATUS RECTUM LENGTH OFLATU S RECTUM EQUATION OF PARABOLA RIGHT LEFT UPWARD DOWNWARD
- 24. Sample Problem