Algebra 2, Unit 8: Conic Sections. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is a conic section?
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A curve formed by the intersection of a plane and a double cone- What are the four main types of conic sections?
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Circle, ellipse, parabola, and hyperbola- What is the standard equation of a circle centered at the origin?
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x^2 + y^2 = r^2- What does 'r' represent in a circle's equation?
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The radius- What is the standard equation of a circle centered at (h, k)?
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(x - h)^2 + (y - k)^2 = r^2- What is an ellipse?
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A conic section forming an oval shape, with two foci- What is the standard equation of an ellipse centered at the origin?
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x^2/a^2 + y^2/b^2 = 1- What are the foci of an ellipse?
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Two fixed points inside the ellipse used to define its shape- What is the major axis of an ellipse?
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The longer axis, passing through both foci- What is the minor axis of an ellipse?
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The shorter axis, perpendicular to the major axis- What is a parabola, as a conic section?
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A curve formed by all points equidistant from a fixed point (focus) and a line (directrix)- What is the focus of a parabola?
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A fixed point used to define the curve- What is the directrix of a parabola?
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A fixed line used to define the curve- What is the standard equation of a parabola opening upward with vertex at the origin?
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y = x^2/(4p), where p is the distance to the focus- What is a hyperbola?
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A conic section with two separate curves (branches), defined by a constant difference of distances to two foci
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