Ellipses: Standard Form definitions Flashcards
Ellipses: Standard Form definitions
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Ellipse A conic section formed by slicing a cone at a slight angle, resulting in a closed, oval-shaped curve with two axes of different lengths. Conic Section A curve obtained by intersecting a cone with a plane, producing shapes like circles, ellipses, parabolas, and hyperbolas. Semi-Major Axis The longest radius of an ellipse, extending from the center to the furthest point on the curve along the major axis. Semi-Minor Axis The shortest radius of an ellipse, extending from the center to the closest point on the curve along the minor axis. Major Axis The longest diameter of an ellipse, passing through its center and both vertices, aligned with the semi-major axis. Minor Axis The shortest diameter of an ellipse, passing through its center and perpendicular to the major axis. Vertex A point on an ellipse located at the maximum distance from the center along the major axis. Foci Two fixed points inside an ellipse where the sum of the distances to any point on the ellipse remains constant. Center The midpoint of both the major and minor axes of an ellipse, serving as the reference for its position. Standard Form An equation format for ellipses, showing squared terms of x and y divided by squared axis lengths, set equal to one. Orientation The direction in which the major axis of an ellipse is aligned, either horizontally or vertically. Denominator The value under each squared variable in the ellipse equation, representing the square of the corresponding axis length. Shift A translation of the ellipse's center from the origin to a new point, indicated by h and k in the equation. C Value The distance from the center of an ellipse to each focus, calculated using the relationship c² = a² - b². Function Transformation A change in the position or shape of a graph, such as shifting the center of an ellipse using h and k.
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