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AATS Section 10.2 Day 1 Notes: Conic Sections – Parabolas Intersecting a plane with a double cone, we get curves known as CONIC SECTIONS. Depending on how the plane and double cone intersect, we can get a CIRCLE, PARABOLA, ELLIPSE, or HYPERBOLA. All of the conic sections are plane figures and can be represented in a coordinate plane. Throughout this chapter we will be learning about each of the four conic sections. Today we will start with PARABOLAS. Definition: A parabola is the set of all points in a plane that are the same distance from a fixed line (the directrix) and a fixed point not on the line (the focus). Important Parts of a Parabola: Standard Equation of a Parabola: Opens Up/Down 2 x h 4c y k Opens Left/Right 2 y k 4c x h c 0 opens up c 0 opens down c 0 opens right c 0 opens left Vertex is h, k “c” is the distance from the vertex to the focus/directrix Identify the vertex, the focus, and the directrix of the parabola with the given equation. Then sketch a graph of the parabola. x 2 8 y 3 1) y 2 12 x 2) Vertex: _______________ Vertex: _______________ Focus: ________________ Focus: ________________ Directrix: _______________ Directrix: _______________ 3) x 3 2 20 y 2 4) y 2 6 x 1 Vertex: _______________ Vertex: _______________ Focus: ________________ Focus: ________________ Directrix: _______________ Directrix: _______________