Ellipses: Standard Form definitions Flashcards
Ellipses: Standard Form definitions
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Ellipse A conic section formed by slicing a cone at an angle, resulting in a closed, oval shape defined by 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. Semi-Minor Axis The shortest radius of an ellipse, extending from the center to the closest point on the curve. Horizontal Ellipse An ellipse oriented so its major axis runs left to right, with the larger denominator under the x-term in its equation. Vertical Ellipse An ellipse oriented so its major axis runs up and down, with the larger denominator under the y-term in its equation. Standard Form An equation format for ellipses showing squared terms of x and y divided by squared axes lengths, set equal to one. Center The midpoint of an ellipse, located at (h, k) in the shifted standard form equation. Vertex A point on the ellipse located at the ends of the major axis, representing the maximum distance from the center. Focus One of two fixed points inside an ellipse where the sum of distances to any point on the curve remains constant. Major Axis The longest line segment passing through the center and both vertices of an ellipse. Minor Axis The shortest line segment passing through the center and both endpoints perpendicular to the major axis. Denominator The squared value under each variable in the standard form equation, representing the square of the axis length. Distance c The value found using c² = a² - b², representing the distance from the center to each focus along the major axis. Function Transformation A shift or change in the graph of an equation, such as moving the center of an ellipse from the origin to (h, k).