(x2+y2)2 = xy
differentiating w.r.t. x
⇒ 2 (x2+y2) (2x+2y

dy

dx

) = y + x

dy

dx

⇒ 4x3+4x2yy

dy

dx

+ 4y2x + 4y3

dy

dx

- y - x

dy

dx

= 0
⇒ (4x2y+4y3−x)

dy

dx

+ 4x3+4y2x - y = 0
⇒ (4x2y+4y3−x)

dy

dx

= - 4x3−4y2x + y
⇒

dy

dx

=

−4x3−4y2x+y

4x2y+4y3−x

OR
x = a (2θ - sin 2θ)
y = a (1 - cos θ)
differentiating w.r.t. θ

dx

dθ

= a (2 - cos 2θ × 2)

dy

dθ

= a (+ sin 2θ × 2)

dy

dx

=

(+sin2θ×2)

(−2cos2θ×2)

=

(sin2θ)

(1−cos2θ)

dy

dx

=

2sinθ×cosθ

2sin2θ

dy

dx

=

cosθ

sinθ

= cot θ
at , θ =

π

3

dy

dx

= cot

π

3

=

1

√3