If (x^2+y^2) ^2=x y, then \frac{d y}{d x} is

Correct Answer is : y−4x(x2+y2)4y(x2+y2)−x

\frac{y+4 x (x^2+y^2) }{4 y (x^2+y^2) -x}

\frac{y-4 x (x^2+y^2) }{x+4 (x^2+y^2) }

\frac{y-4 x (x^2+y^2) }{4 y (x^2+y^2) -x}

\frac{4 y (x^2+y^2) -x}{y-4 x (x^2+y^2) }

CBSE Class 12 Math 2022 Term I Solved Paper - Question 8

Question : 8 of 50

Marks: +1, -0

(x^2+y^2) ^2=x y

, then

\;{d y}/{d x}

Solution:

Explanation: Given,

(x^2+y^2) ^2=x y

⇒ \;\; x^4+2 x^2 y^2+y^4-x y=0

Differentiating w.r.t.

x

, we get

4 x^3+2 [2 x y^2+x^2 ⋅ 2 y \;{d y}/{d x}] +4 y^3 \;{d y}/{d x}- [y+x \;{d y}/{d x}] =0

\;{d y}/{d x} [4 x^2 y+4 y^3-x] + [4 x^3+4 x y^2-y] =0

\;{d y}/{d x}=\;{- [4 x^3+4 x y^2-y] }/{ [4 x^2 y+4 y^3-x] }

\;\text " or "\; \;\; \;{d y}/{d x}=\;{y-4 x (x^2+y^2) }/{4 y (x^2+y^2) -x}

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