Find the locus of the mid-point of the portion of the line `xcosalpha+ysinalpha=p` which is intercepted between the axes.

Explanation

Let the line cut the axes in A and B and if `(h,k)` be the midpoints of AB, then

`2h=p/(costheta​),2k=p/(sintheta)`
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thus,`cos^2(theta)+sin^2(theta)=1`

`=>(p^2)/(4h^2)+(p^2)/(4k^2)=1`


`=>1/(4h^2)+1/(4k^2)=1/(p^2)`

`=>1/(h^2)+1/(k^2)=4/(p^2)`

`=>1/(x^2)+1/(y^2)=4/(p^2)`
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