This is question 20, Exercise 6C.
"Find the equations of the four tangents common to the hyperbola x^2 - 2y^2 = 4 and the circle x^2 + y^2 = 1. Find the points of contact of these tangents with the circle." [Hint: Let xx1 + yy1 = 1 be tangent to x^2 + y^2 = 1 at P(x1, y1)]
Here's what I tried...