Q. 185.0( 3 Votes )

Find the locus of

Answer :

Given:


Line x sin θ + y cos θ = p


To find:


The locus of the mid-points of the portion of the line x sin θ + y cos θ = p intercepted between the axes.


Explanation:


If the equation of the given line is


x sin θ + y cos θ = p, then the solution is shown below:


The line


x sin θ + y cos θ = p intercepts the axes.


Thus, the coordinate of the poin where the line intercepts x – axis is



Thus, the coordinate of the poin where the line intercepts y – axis is



The midpoint R of the line is given by


R(h, k)


h , k


Eliminating the sine and cosine terms, we get




p2(h2 + k2) = 4h2k2


Thus, the locus is given by


p2(x2 + y2) = 4x2y2


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