Here are the essential concepts you must grasp in order to answer the question correctly.
Ellipse Standard Form
The standard form of the equation of an ellipse is given by the formula (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center of the ellipse, 'a' is half the length of the major axis, and 'b' is half the length of the minor axis. This form allows for easy identification of the ellipse's dimensions and orientation.
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Major and Minor Axes
The major axis of an ellipse is the longest diameter, while the minor axis is the shortest. In this case, the major axis is horizontal with a length of 8, meaning 'a' equals 4. The minor axis has a length of 4, so 'b' equals 2. These axes determine the shape and size of the ellipse.
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Center of the Ellipse
The center of an ellipse is the midpoint of both the major and minor axes. For this problem, the center is given as (0, 0), which means the ellipse is symmetrically positioned around the origin of the coordinate plane. This information is crucial for correctly placing the ellipse in the standard form equation.
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Graph Ellipses NOT at Origin