find the locus of the mid point of the portion of the line x cosa +yp sin a = p which is intercepted between the axis ??

If the equation of the given line is , then the solution is shown below:

The line intercepts the axes. 

Thus the coordinate of the point where the line intercepts x-axis is , and the coordinate of the point where the line intercepts y-axis is . The mid-point R of the line is given by

Eliminating the sine and cosine terms, we get

Thus, the locus is given by

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