Question
The locus of the midpoint of te portion intercepted between the axes by the line where p is constant is

x^{2} + y^{2} = 4p^{2}



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Solution
Let the line meet the xaxis and yaxis respectivelyA and B. then coordinates of A are and those of B are . If (h, k)is the midpoint of AB, then
To find the locus of (h, k) we have to eliminate . We have
And
Whence squaring and adding, we get
.
the required locus of (h, k) is
or
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