x^2+xy+y^2=49 - Wolfram|Alpha

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Input

x^2 + x y + y^2 = 49

Alternate form

x^2 + x y + y^2 - 49 = 0

(x + y/2)^2 + 1/4 (3 y^2 - 196) = 0

Real solutions

x = -14/sqrt(3), y = 7/sqrt(3)

x = 14/sqrt(3), y = -7/sqrt(3)

Solutions

y = 1/2 (-sqrt(196 - 3 x^2) - x)

y = 1/2 (sqrt(196 - 3 x^2) - x)

Implicit derivatives

(dx(y))/(dy) = -(x + 2 y)/(2 x + y)

(dy(x))/(dx) = -(2 x + y)/(x + 2 y)

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