Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Form of an Ellipse
The standard form of an ellipse is given by the equation (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center of the ellipse, a is the semi-major axis, and b is the semi-minor axis. This form helps identify the orientation and dimensions of the ellipse, which is crucial for graphing it accurately.
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Foci of an Ellipse
The foci of an ellipse are two fixed points located along the major axis, which are essential for defining the shape of the ellipse. The distance from the center to each focus is calculated using the formula c = √(a² - b²), where c is the distance to the foci, a is the semi-major axis, and b is the semi-minor axis.
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Foci and Vertices of an Ellipse
Graphing an Ellipse
Graphing an ellipse involves plotting its center, determining the lengths of the semi-major and semi-minor axes, and marking the foci. The ellipse is then drawn by connecting the points that satisfy the ellipse equation, ensuring the correct shape and orientation based on the values of a and b.
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