Question

The equation of a curve is xy=12 and the equation of a line L is zx+y=k, where k is constant.
i) In the case k=1 find the coordinates of the points of intersection of L and the curve.
ii) Find the set of values of k for which L does not intersect the curve.
iii) In the case where k=10, one of the points of intersection is P(2,6). Find the angle in degrees between L and the tangent to the curve at P.