)2, which is a circle. (Q) If |z−z1|−|z−z2| = k, where < |z1−z2|, the locus is a hyperbola. (R) Let t = tan α. Hence, x = √3cos2α and y = sin 2α or cos 2α =
x
√3
and sin 2α = y
x3
3
+y2 = sin22α+cos22α = 1, which is an ellipse (S) If eccentricity is [1, ∞), then the conic can be a parabola (if e = 1) and a hyperbola if e ∈ (1,∞). (T) Let z = x + iy; x, y ∈ R. Hence, (x+1)2−y2 = x2+y2+1 ⇒ y2 = x; which is a parabola.