Question

15. If f(x, y) = x^3 + y^2 - 3axy = 0,
dy
can be found out as
dx
ay+x
ay-x
a)
y tax
b)
ay-x?
y--ax
c)
d) none of these
y tax​

Answer 1

Given, x

2

+y

3

=3axy...(1)

Differentiating equation,

⇒3x

2

+3y

2

dx

dy

=3a(x

dx

dy

+y)

⇒3x

2

+3y

2

dx

dy

=3ax

dx

dy

+3ay

⇒(3y

2

−3ax)

dx

dy

=3ay−3x

2

⇒3(y

2

−ax)

dx

dy

=2(ay−x

2

)

⇒

dx

dy

=

y

2

−ax

ay−x

2

Given, x

2

+y

3

=3axy...(1)

Differentiating equation,

⇒3x

2

+3y

2

dx

dy

=3a(x

dx

dy

+y)

⇒3x

2

+3y

2

dx

dy

=3ax

dx

dy

+3ay

⇒(3y

2

−3ax)

dx

dy

=3ay−3x

2

⇒3(y

2

−ax)

dx

dy

=2(ay−x

2

)

⇒

dx

dy

=

y

2

−ax

ay−x

2

Given, x

2

+y

3

=3axy...(1)

Differentiating equation,

⇒3x

2

+3y

2

dx

dy

=3a(x

dx

dy

+y)

⇒3x

2

+3y

2

dx

dy

=3ax

dx

dy

+3ay

⇒(3y

2

−3ax)

dx

dy

=3ay−3x

2

⇒3(y

2

−ax)

dx

dy

=2(ay−x

2

)

⇒

dx

dy

=

y

2

−ax

ay−x

2