Question

if x2+y2=t−1t andx4+y4=t2+1t2then prove that dydx=1x3y

Answer 1

Answer:

here your answer..✌️✌️

Answer

We have,

x

2

+y

2

=t−

t

1

and x

4

+y

4

=t

2

+

t

2

1

⇒(x

2

+y

2

)

2

=(t−

t

1

)

2

⇒x

4

+y

4

+2x

2

y

2

=t

2

+

t

2

1

−2

⇒x

4

+y

4

+2x

2

y

2

=x

4

+y

4

−2 [given]

⇒2x

2

y

2

=−2

⇒x

2

y

2

=−1

⇒y

2

=−

x

2

1

⇒y

2

=−x

−2

Differentiating w.r.t. x, we get,

⇒2y

dx

dy

=−(−2)x

−3

⇒y

dx

dy

=

x

3

1

∴

dx

dy

=

x

3

y

1

Answer 2

if x2+y2=t−1t andx4+y4=t2+1t2then prove that dydx=1x3y