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# Lecture #6 analytic geometry

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### Lecture #6 analytic geometry

1. 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. 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. 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)
4. 4. PARTS OF PARABOLA
5. 5. GRAPHS OF PARABOLA  The graph of parabola if the vertex is at the origin, and opens to the right,
6. 6.  The graph of parabola if the vertex is at the origin, and opens to the left,
7. 7.  The graph of parabola if the vertex is at the origin, and opens upward,
8. 8.  The graph of parabola if the vertex is at the origin, and opens downward,
9. 9.  The graph of parabola if the vertex is at (h, k) , and opens to the right,
10. 10.  The graph of parabola if the vertex is at (h, k) , and opens to the left,
11. 11.  The graph of parabola if the vertex is at (h, k) , and opens upward,
12. 12.  The graph of parabola if the vertex is at (h, k) , and opens downward,
13. 13. EQUATIONS OF PARABOLA 
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22. 22. FORMULAS VERTEX AT (0, 0 ) FOCUS DIRECTRIX ENDS OF LATUS RECTUM LENGTH OF LATUS RECTUM EQUATION OF PARABOLA RIGHT LEFT UPWARD DOWNWARD
23. 23. FORMULAS VERTEX AT (h, k) FOCUS DIRECTRIX ENDS OF LATUS RECTUM LENGTH OFLATU S RECTUM EQUATION OF PARABOLA RIGHT LEFT UPWARD DOWNWARD
24. 24. Sample Problem 