Question

find the area of loop of the curve x^4 -2axy+a^2y^2=0​

Answer 1

Answer:

4y 2=x

2

(4−x 2 )

⇒y=± 21

x

2

(4−x

2

)

⇒y=±

2

x

(4−x

2

)

Therefore, Area(A)=4×∫

0

2

2

x

4−x

2

dx

Let 4−x

2

=t⇒−2xdx=dt

⇒A=∫

0

4

t

dt=[

3/2

t

3/2

]

0

4

⇒A=

3

2

64

⇒A=

3

16

sq.units