3. PARABOLA.pptx

Parabola Conic Sections - Parabola The intersection of a plane with one nappe of the cone is a parabola. Conic Sections - Parabola The parabola has the characteristic shape shown above. A parabola is defined to be the “set of points the same distance from a point and a line”. Conic Section...

Parabola Conic Sections - Parabola The intersection of a plane with one nappe of the cone is a parabola. Conic Sections - Parabola The parabola has the characteristic shape shown above. A parabola is defined to be the “set of points the same distance from a point and a line”. Conic Sections - Parabola Focus Directrix The line is called the directrix and the point is called the focus. Conic Sections - Parabola Focus y = ax2 p p Directrix The distance from the vertex to the focus and directrix is the same. Let’s call it p.  axis of symmetry line perpendicular to the directrix passing through the focus vertex is the point of intersection of the axis of symmetry with the parabola. Equation of parabola with vertex at the origin and focus at (p, 0) y2 = 4px If p > 0, the parabola opens to the right. If p < 0, the parabola opens to the left. Equation of parabola with vertex at the origin and focus at (0, p) x2 = 4py If p > 0, the parabola opens upward. If p < 0, the parabola opens downward. Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the given equation. Sketch the graph, and include these points and lines. 1. y2 = -12x 2. 2x2 – 14y = 0 Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the given equation. Sketch the graph, and include these points and lines. 1. y2 = 6x 2. x2 = -10y 3. 2y2 = 9x 4. y2 + 7x = 0 5. 3x2 – 4y = 0 Equation of parabola with vertex at (h, k) and focus at (h+p, k) (y – k)2 = 4p(x – h) (vertex form) If p > 0, the parabola opens to the right. If p < 0, the parabola opens to the left. Equation of parabola with vertex at (h, k) focus at (h, k+p) (x – h)2 = 4p(y – k) (vertex form) If p > 0, the parabola opens upward. If p < 0, the parabola opens downward. Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the given equation. Sketch the graph, and include these points and lines. 1. x2 – 6x – 12y – 51 = 0 2. y2 + 8x – 6y + 25 = 0 Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the given equation. Sketch the graph, and include these points and lines. 1. y2 + 8y + 6x + 16 = 0 2. x2 – 8x – 6y – 8 = 0 End