Polar hypersurface explained

C

described by the homogeneous equation

f(x0,x1,x2,...)=0

and a point

a=(a0:a1:a2: … )

its polar hypersurface

Pa(C)

is the hypersurface

a0f0+a1f1+a2f2+ … =0,

where

fi

are the partial derivatives of

f

.

The intersection of

C

and

Pa(C)

is the set of points

p

such that the tangent at

p

to

C

meets

a

.

References

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