Equation of a Parabola. Do Now  What is the distance formula?  How do you measure the distance from a point to a line?

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Presentation transcript:

Equation of a Parabola

Do Now  What is the distance formula?  How do you measure the distance from a point to a line?

Conic Sections  The different types of cross sections of a plane and a cone are called conic sections.  circle  parabola  ellipse  hyperbola

Conic Sections  One way to write equations for all four of these is by defining them as the set of points with a given ratio of distances from a certain point (or points) and/or line.  For example, a ____________ is the set of points equidistant (1:1 ratio) from a given point.

Parabolas  A parabola can be defined as the set of all points equidistant from a given point, called the ___________, and a given line, called the ____________.  Let the vertex be (0, 0).  Let the focus be (0, p). Then the directrix is ________.

Example 1— Given Focus  Write the equation of the parabola with vertex at (0, 0) and focus at (0, 3). (Use x 2 = 4py.)

Example 2— Given Directrix  Write the equation of the parabola with vertex at (0, 0) and directrix at y = -5. (Use x 2 = 4py.)