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Conics: Standard Form Pre-Calculus Conics part 1

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PARABOLA A parabola is the set of all points (x, y) in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.

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Standard Form of a Parabola

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Find the standard form of the following:

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Circle A circle is the set of all points in space that are a given distance from a fixed point called the center.

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Standard form of a Circle

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Find the standard form:

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Ellipse The line through the foci intersects the ellipse at two points called vertices. The chord joining the vertices is the major axis, and its midpoint is the center of the ellipse. The chord perpendicular to the major axis through the center of the ellipse is the minor axis of the ellipse. It intersects the ellipse at its co-vertices.

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Standard Form of an Ellipse Given 0 < b < a

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Write in standard form:

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HYPERBOLA A hyperbola has two disconnected branches. The line through the foci intersects the hyperbola at its two vertices and is called the transverse axis. The midpoint of the transverse axis is the center of the hyperbola.

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Standard Form of a Hyperbola a is not largest value, but first denominator

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Write in standard form:

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SUMMARIZE… How can you determine what type of conic section an equation represents from the generic formula… Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 Parabolax is squared or y is squared, but not both Circle Ellipse Hyperbola

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Classify each equation.

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