# A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment lies a units from one end and b units from the other end. Show that P traces an ellipse as the ends of the segment slide along the axes.

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A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment lies a units from one end and b units from the other end. Show that P traces an ellipse as the ends of the segment slide along the axes.

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Step 1

Given A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment lies a units from one end and b units from the other end

Step 2

First make the sketch and let the segment a+b intersect the y axis in point A and intersect the x axis in point B

Step 3

Then

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