Normals from a Point to a Quadric in N Dimensions

Using Cartesian co-ordinates, the equation to a quadric in N dimensions may, in general, be reduced to a₁ X₁² + a₂x₂² + + a_nx_n² = 1. .....            (1)

Let P be any point (α₁, α₂, ... α_n); consider the locus of points Q whose polar planes with respect to (l) are perpendicular to PQ.