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An ellipse on the xy-plane has foci at (-41, 23) and (115, 42). The ellipse is tangent to the x-axis. What is the length of the major axis of the ellipse?
An ellipse is a geometric shape that resembles a flattened circle. It is defined as a closed curve in which the sum of the distances from any point on the curve to two fixed points (called foci) is constant.
The major axis of an ellipse is the longest diameter of the ellipse, passing through the center and connecting two opposite points on the boundary of the ellipse. It is also known as the longest axis or the major diameter.
The length of the major axis of an ellipse can be calculated using the formula 2a, where a is the semi-major axis. The semi-major axis is half of the major axis and is equal to the distance from the center of the ellipse to the furthest point on the ellipse in any direction.
Yes, the length of the major axis of an ellipse can change. It depends on the eccentricity of the ellipse, which is a measure of how elongated the ellipse is. A higher eccentricity results in a longer major axis, while a lower eccentricity results in a shorter major axis.
An ellipse and a circle are both closed curves, but an ellipse is elongated while a circle is perfectly round. The major axis of an ellipse is longer than the minor axis, while the diameter of a circle is the same throughout. Additionally, a circle has an eccentricity of 0, while an ellipse has an eccentricity between 0 and 1.