1, hyperbola has two asymptotes, and point P is not on the asymptote, so parallel lines passing through point P as asymptotes must intersect hyperbola at one point, and at the same time, this point is on the convex surface of hyperbola and can be tangent to two branches of hyperbola respectively, so there are four * * *.

2. A parabola has no asymptote, and any straight line parallel to its symmetry axis intersects the parabola at one point. At the same time, points outside the parabola can also lead to two tangents. So one * * * has three.

For conic curves, there are several cases where a straight line passes through any point and has only one intersection with the curve: for ellipses, there are 2 (two tangents) outside the ellipse, 1 (a tangent) on the ellipse and 0 inside the ellipse; For hyperbola, there are three on the hyperbola (one tangent and two parallel to the asymptote), two on the asymptote (one tangent and one parallel to the other asymptote), the center of symmetry is 0, the points between hyperbolas except asymptote 4 (two tangents and two parallel to the asymptote), and two on both sides of the hyperbola (two parallel to the asymptote); For parabola, parabola outer 3 (two tangents, one parallel symmetry axis), parabola outer 2 (one tangent, one parallel symmetry axis), parabola inner 1 (one parallel symmetry axis).