(a,b,c,d)

Let (r, θ ) be the polar co-ordinates of any point P on the curve where r is the distance of the point from origin

∴ r 2 [5 (cos 2 θ + sin 2 θ ) – 8 sin θ . cos θ ] = 4

∴ r 2 =

r 2 is maximum when 5 – 4 sin 2 θ is minimum

= 5 – 4 = 1 when sin 2 θ = 1

∴ 2 θ = 90 0 ∴ θ = 45 0 ∴ r = ± 2, θ = 45

0 …(1)

Again r 2 is minimum when 5 – 4 sin 2 θ is maximum = 5 + 4 = 9 when sin 2 θ = –1

∴ 2 θ = ∴ θ =

∴ r = ± , θ = … (2)

Hence the points are (r cos θ , r sin θ ) where r, θ are given by (1) and (2). Thus we get the four points given in , , , .