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Conics: Parabolas

Conics: Parabolas. Parabolas:. The set of all points equidistant from a fixed line called the directrix and a fixed point called the focus . The vertex is the point midway between the focus and the directrix . The line that connects the vertex and the focus is the axis of symmetry.

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Conics: Parabolas

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  1. Conics: Parabolas

  2. Parabolas: • The set of all points equidistant from a fixed line called the directrix and a fixed point called the focus. • The vertex is the point midway between the focus and the directrix. • The line that connects the vertex and the focus is the axis of symmetry.

  3. The standard form equation of a parabola with vertex at (h, k) is The first equation is for a parabola that opens up or down. The second equation is for a parabola that opens left or right.

  4. If the equation is • The focus is the point . • The directrix is the line. • The axis of symmetry is parallel to the y-axis (vertical).

  5. If the equation is • The focus is the point . • The directix is the line . • The axis of symmetry is parallel to the x-axis (horizontal).

  6. Latus Rectum • The latus rectum is a line segment through the focus, parallel to the directrix. • The endpoints of the latusrectum are each a distance of 2a from the focus.

  7. Ex. 1 Find the vertex, focus and directrix of the parabola. Graph the equation. a)

  8. b)

  9. c)

  10. d)

  11. Ex.2 Write the equation of the parabola. a) Vertex: (0, 0), focus: (-4, 0)

  12. b) Directrix: y = 6, vertex: (0, 0)

  13. c) Directrix: x = -4, focus: (2, 4) Hint: start with a sketch of the graph.

  14. d) Vertex: (3, 0), focus: (3, -2)

  15. Ex. 3 Write the equation of the parabola with the given vertex and point on the parabola. • a) Vertex: (1, 0) Point: (0, 1)

  16. b) Vertex: (1, -1) Point: (0, 1)

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