The locus of the centres of circles passing through the origin and intersecting the fixed circle...

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The locus of the centres of circles passing through the origin and intersecting the fixed circle \( x^{2}+ \) \( y^{2}-5 x+3 y-1=0 \) orthogonally is
(a) a straight line of the slope \( \frac{3}{5} \)
(b) a circle
(c) a pair of straight lines
(d) none of these
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