Tangents Passing Through the Inner or Exterior Point of a Non-degenerate Quadric Curve

Firstly, this paper generally gives a tangent equation of a quadratic curve Γ,where the tangent passes through an arbitrary point M0 on R2 plane,then offers a definition of a nondegenerate quadric curve's inner region and exterior region, gives the necessary and sufficient conditions and a equation of that Γ has two real or imaginary tangents passing through the point M0not on Γ. The decision condition is given by calculating the sign of I3F(x0,y0) .