Q:
# What are the methods for graphing ellipses?

An ellipse is graphed in a coordinate plane by determining its center and the x- and y-coordinates for one point along the ellipse and then plugging those values into an appropriate formula. One formula for graphing an ellipse is (x - h)^2/a^2 + (y - k)^2/b^2 = 1.

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In the formula for graphing the ellipse, the variable h is the x-coordinate of the center, k is the y-coordinate of the center, a is the distance from the center to the edge of the ellipse along the major axis, and b is the distance from the center to the edge of the ellipse along the minor axis. The major axis of the ellipse is the line that runs through the center of an ellipse at its longest part, whereas the minor axis is the line that runs through the center of the ellipse perpendicular to the major axis.

The points where the major axis intersects the ellipse are called the vertices, while the points where the minor axis intersects are called the co-vertices. Use these four points and the center to graph the ellipse, verifying the coordinates with the formula.

Another formula that can be used to graph an ellipse is x^2/a^2 + y^2/b^2, although this formula is used when the center of the ellipse is not known.

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