(a) Find the centre of curvature of the curve $x^{2}+y^{2}=2$ at the point ( 1,1 ).
Explanation
The centre of curvature of a curve at a point is given by the formula $C = \left( x - rac{y y_{1}}{y_{1}^{2} + x_{1}^{2}}, y + rac{x x_{1}}{y_{1}^{2} + x_{1}^{2}} ight)$.
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