Find the centre of curvature y^2=4ax at (x,y)
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Let (bar x, bar y) be the centre of curvature at the point (at2, 2at) of this curve. the locus of the centre of curvature is the curve This curve meets the axis of x in the point (2a, 0). It also meets the parabola where and therefore Hence it meets the parabola at the points The curve is called a semi-cubical parabola and could be shewn to be of the shape of the dotted curve in the figure.
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