Hyperbolas NOT at the Origin definitions Flashcards
Hyperbolas NOT at the Origin definitions
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Hyperbola A conic section with two separate branches, defined by a specific quadratic equation involving subtraction of squared terms. Conic Sections The four main curves—circle, ellipse, parabola, and hyperbola—formed by intersecting a plane with a cone. Standard Equation A mathematical form representing a hyperbola, modified by shifting parameters to indicate its center. Center The point (h, k) indicating the location around which a hyperbola is symmetrically arranged. Horizontal Shift A movement of the hyperbola along the x-axis, determined by the value subtracted from x in the equation. Vertical Shift A movement of the hyperbola along the y-axis, determined by the value subtracted from y in the equation. Vertices The two points on a hyperbola closest to or farthest from the center, found by adjusting one coordinate by 'a'. Asymptotes Diagonal lines that the branches of a hyperbola approach but never touch, aiding in sketching the curve. Foci Two fixed points inside each branch of a hyperbola, located using the relationship c² = a² + b². Branches The two separate, mirror-image curves that make up a hyperbola, each approaching the asymptotes. a Value The positive square root of the denominator under the leading squared term, used to find vertices. b Value The positive square root of the denominator under the second squared term, used to find 'b' points. c Value The distance from the center to each focus, calculated using c² = a² + b². Box Method A graphical technique using a rectangle formed by vertices and 'b' points to help draw asymptotes. Vertical Hyperbola A hyperbola oriented so its branches open up and down, indicated when the y-term appears first in the equation.
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