數學難題 - 高中級

1. The curves y = (4/x) + 2 and y = ax^2 + bx + c intersect and have a common tangent at x=2
a) If the curves also intersect at P(1,6), calculate the vertex of the parabola.
b) Prove that there are only two points of intersection of these curves.

2. Given the two parabolas y = 2 - x^2 and y = 5 + x^2, determine the equations of all common tangent lines. Leave your answers in simplified radical form. Do not use decimals to approximate the solution. It may be helpful to sketch the graphs too see the situation.