Find the locus of the midpoint of the chords of circle `x^(2)+y^(2)=a^(2)` having fixed length l.
Text Solution
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As shown in the figure, AB is one of the variable chords having length l. Let the midpoint of AB is M(h,k) . The foot of perpendicular from centre C on AB is M. In right angles triangled CMA, we have `AC^(2)=CM^(2)+AM^(2)` `:. a^(2)=(h^(2)+k^(2))+((l)/(2))^(2)` Hence, equation of required locus is `x^(2)+y^(2)=a^(2)-(l^(2))/(4)`.
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