Question

the graph shows an ellipse. what are the lengths of its major and minor axes? length of major axis = length of minor axis =

Explanation:

Step1: Determine the major axis length

The major axis is the longer axis of the ellipse. The endpoints of the major axis are at \(y = 4\) and \(y=-6\).
The distance between \(y_1 = 4\) and \(y_2=-6\) is calculated using the formula \(d=\vert y_1 - y_2\vert\).

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Step2: Determine the minor axis length

The minor axis is the shorter axis of the ellipse. The endpoints of the minor axis are at \(x=-8\) and \(x = 6\).
The distance between \(x_1=-8\) and \(x_2 = 6\) is calculated using the formula \(d=\vert x_1 - x_2\vert\).

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Answer:

Length of major axis = \(14\)
Length of minor axis = \(10\)