High Quality Content by WIKIPEDIA articles! The cruciform curve, or cross curve is a quartic plane curve given by the equation x^2y^2-b^2x^2-a^2y^2=0 , where a and b are two parameters determining the shape of the curve. The cruciform curve is related by a standard quadratic transformation, x ? 1/x, y ? 1/y to the ellipse a2x2 + b2y2 = 1, and is therefore a rational plane algebraic curve of genus zero. The cruciform curve has three double points in the real projective plane, at x=0 and y=0, x=0 and z=0, and y=0 and z=0.

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