Equations of locus

Given a circle C:x^2 +y^2 = 8.
Let L:y = mx+c be a tangent to C.

a. Show that C^2 = 8m^2 +8.
b. Suppose L passes through the point (h,k).
Use the result (a), show that (h^2 -8)m^2 - 2hkm +(k^2 -8) = 0.
c. Two tangents with slopes m1 and m2 are drawn from the point(4,6) to C.
Find the acute angle between the two tangents.
Correct your answer to the nearest degree.
d. P is a variable point outside C and the two tangents from P to C are
at right angle.
Find the equation of the locus of P when M moves.