Polar hypersurface

In algebraic geometry, given a projective algebraic hypersurface C described by the homogeneous equation

f(x_0,x_1,x_2,\dots) = 0 \,

and a point

a = (a_0:a_1:a_2: \dots),

its polar hypersurface P_a(C) is the hypersurface

a_0 f_0 + a_1 f_1 + a_2 f_2+\cdots = 0, \,

where ƒ_i are the partial derivatives.

The intersection of C and P_a(C) is the set of points p such that the tangent at p to C meets a.

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