A straight line AB of length 10 units is free to move with its end on the axes.find the locus of the point p(x,y) on the line at the distance of 3 units from the end on the x-axis

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  1. I am wondering where is the end of an axis, all those I draw have no ends. x axis is not a line segement.

    What do you mean by the end of the axis?

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  2. The line segment touches bot the x- and y-axes at all times. So, the point p is 3 units away from the x-axis, along the line.

    So, let the line make an angle θ with the x-axis (measured clockwise).

    Then picture point P as being at the end of a rod of length 7, which slides down the y-axis.

    x = 7cosθ
    y = 3sinθ

    The graph is an ellipse.

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