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.

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Presentation transcript:

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.

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.

If the equation is

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

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

b)

c)

d)

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

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

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

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

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

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