A curve passing through origin, all the normals to which pass through \( \left(x_{0}, y_{0}\righ...

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A curve passing through origin, all the normals to which pass through \( \left(x_{0}, y_{0}\right) \) is
(a) \( y y_{0}=x^{2}+y^{2} \)
(b) a circle with centre \( \left(x_{0}, y_{0}\right) \)
(c) \( x^{2}+y^{2}=x_{0}^{2}+y_{0}^{2} \)
(d) \( x^{2}+y^{2}=\frac{1}{2}\left(x_{0}^{2}+y_{0}^{2}\right) \)
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