Here are the essential concepts you must grasp in order to answer the question correctly.
Ellipse Equation
An ellipse is represented by the standard form of its equation, which is (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis. The values of a and b determine the shape and size of the ellipse, while the orientation depends on whether a² or b² is larger.
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Foci of an Ellipse
The foci of an ellipse are two fixed points located along the major axis, which are crucial for defining the ellipse's shape. The distance from the center to each focus is calculated using the formula c = √(a² - b²), where c is the distance to each focus from the center. This property is essential for understanding the geometric characteristics of the ellipse.
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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 axes are drawn perpendicular to each other, and the ellipse is sketched by connecting the endpoints of the axes in a smooth, oval shape. Understanding the graphing process is vital for visualizing the ellipse and its properties.
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