Verified answer

i) x = 2sin(Ɵ); y = 2sin(2Ɵ) = 2*[2sin(Ɵ)*cos(Ɵ)] {application of multiple angle identity}

Substituting for x = 2sin(Ɵ), y = 2x*cos(Ɵ)

ii) The above reduces to: x/2 = sin(Ɵ) and y/2x = cos(Ɵ)

iii) Squaring and adding both of them, x²/4 + y²/4x² = sin²Ɵ + cos²Ɵ = 1

==> x⁴ + y² = 4x²

==> y² = 4x² - x⁴

y=2 (2 sin Ɵ cos Ɵ)

y = 2 x sqrt(1-sin^2 Ɵ)

y = 2 x sqrt( 1- 4 sin^2 Ɵ /4)

y = 2 x sqrt( 1-x^2 /4)

y= 2 x sqrt(4-x^2) /2

y= x sqrt(4-x^2)