What is $\frac{dy}{dx}$ if $x^2+xy+y^2=1

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

What is $\frac{dy}{dx}$ if $x^2+xy+y^2=100$

Options:

$\frac{2x+y}{x+y}$

$\frac{-2x-y}{x+2y}$

$\frac{x+2y}{x+y}$

$\frac{x-y}{x+y}$

Correct Answer:

$\frac{-2x-y}{x+2y}$

Explanation:

$x^2+xy+y^2=100$

differentiating wrt x

$2x+y+x\frac{dy}{dx}+2y\frac{dy}{dx}=0$

so $\frac{dy}{dx}=\frac{-2x-y}{x+2y}$