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 )

4. PARTS OF PARABOLA

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,

13. EQUATIONS OF PARABOLA If the parabola opens to the right, with vertex at the origin, the equation is  

14. If the parabola opens to the left, with vertex at the origin, the equation is  

15. If the parabola opens upward, with vertex at the origin, the equation is  

16. If the parabola opens downward, with vertex at the origin, the equation is  

17. If the parabola opens to the right, with vertex at (h, k), the equation is  

18. If the parabola opens to the left, with vertex at (h, k), the equation is  

19. If the parabola opens upward, with vertex at (h, k), the equation is  

20. If the parabola opens downward, with vertex at (h, k), the equation is  

21. The general equation of parabola is given by Or  

22. FORMULAS VERTEX AT (0, 0 ) FOCUS DIRECTRIX ENDS OF LATUS RECTUM LENGTH OF LATUS RECTUM EQUATION OF PARABOLA RIGHT LEFT UPWARD DOWNWARD 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 LENGTHOF LATUS RECTUM EQUATION OF PARABOLA RIGHT LEFT UPWARD DOWNWARD VERTEX AT (h, k) FOCUS DIRECTRIX ENDS OF LATUS RECTUM LENGTHOF LATUS RECTUM EQUATION OF PARABOLA RIGHT LEFT UPWARD DOWNWARD

24. Sample Problem Find the vertex, focus, length of the latus rectum, ends of the latus rectum and hence graph the parabola.