P-is-the-point-representing-the-complex-number-z-r-cos-i-sin-in-an-argand-diagram-such-that-z-a-z-a-a-2-Show-that-P-moves-on-the-curve-whose-equation-is-r-2-2a-2-cos2-sketch-t

Question Number 94081 by Rio Michael last updated on 16/May/20

P is the point representing the complex number

z = r (\cos θ + i \sin θ) in an argand diagram such

that ∣ z - a ∣∣ z + a ∣ = a^{2} . Show that P moves on the curve

whose equation is r^{2} = 2 a^{2} \cos 2 θ . sketch the curve

r^{2} = 2 a^{2} \cos 2 θ, showing clearly the tangents at the pole .