Given that point P is a point outside circle C: x2 + y2 = 1, let K1 and K2 be the slopes of two tangent lines of circle C passing through point P respectively. (1) if point P coordinates are (2, 2), find the value of K1 · K2; (2) if K1 · K2 = - λ (λ≠ - 1, 0), find the equation of locus m of point P, and point out the type of conic where curve m lies

Given that point P is a point outside circle C: x2 + y2 = 1, let K1 and K2 be the slopes of two tangent lines of circle C passing through point P respectively. (1) if point P coordinates are (2, 2), find the value of K1 · K2; (2) if K1 · K2 = - λ (λ≠ - 1, 0), find the equation of locus m of point P, and point out the type of conic where curve m lies

(1) Let the tangent slope of point p be K, and the equation be Y-2 = K (X-2), that is, kx-y-2k + 2 = 0; ∵ if it is tangent to a circle, then | 2K − 2 | K2 + 1 = 1, which is reduced to 3k2-8k + 3 = 0, ∵ K1 · K2 = 1