9.2

1. 9.2 Parabolas

2. A parabola is the set of all points P in the plane that are equidistant from a fixed point F (focus) and a fixed line d (directrix).

3. Other definitions: The line that goes through the focus F and perpendicular to the directrix D is called the axis of symmetry. The point of intersection of the parabola with its axis of symmetry is called the vertex V.

4. Equations of parabolas Vertex at (0,0) y2 = 4ax opens to the right, axis of symmetry is the x- axis. Focus is at (a,0) and d-line is at x = -a. y2 = -4ax opens to the left, axis of symmetry is the x-axis Focus is at (-a,0) and the d-line is at x = a.

5. x2 = 4ay opens up, y-axis is the axis of symmetry focus is at (0,a) and d line is at y = -a. x2 = -4ay opens down, y-axis is the axis of symmetry focus is at (0,-a) and d line is at y = a.

6. Parabolas vertex at (h,k) (y-k)2 = 4a(x-h) opens to the right, axis of symmetry is parallel to the x-axis. V (h,k) F (h+a,k) D-line x = h-a (y-k)2 = -4a(x-h) opens to the left, axis of symmetry is parallel to the x-axis. V (h,k) F (h-a,k) D-line x = h+a

7. (x-h)2 = 4a(y-k) opens up, axis of symmetry parallel to the y-axis V(h,k) F(h,k+a) D-line y = k-a (x-h)2 = -4a(y-k) opens down, axis of symmetry parallel to the y-axis V(h,k) F(h,k-a) D-line y = k+a

8. HW pg 673 1-14 all 15-37 odd