Example.57. Find the locus of middle points of chords of the circle $x^2+y^2=a^2$, which subtend right angle at the point (c, 0).

Dear Student,
Please find below the solution to the asked query:

$\mathrm{Let} \mathrm{us} \mathrm{take} \mathrm{general} \mathrm{point} \left(\mathrm{p},\mathrm{q}\right) \mathrm{inplace} \mathrm{of} \left(\mathrm{c},0\right) \mathrm{to} \mathrm{get} \mathrm{general} \mathrm{result}.$




$$\begin{gathered} \mathrm{Put} \mathrm{p}=\mathrm{c} \mathrm{and} \mathrm{q}=0 \mathrm{to} \mathrm{get} \mathrm{your} \mathrm{answer} \\ {\mathrm{x}}^2+{\mathrm{y}}^2-\mathrm{cx}=\frac{1}{2}\left({\mathrm{a}}^2-{\mathrm{c}}^2\right) \end{gathered}$$
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