(x^2+y^2-1*x)^2=1^2*(x^2+y^2). - Wolfram|Alpha

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Input

(x^2 + y^2 - 1 x)^2 = 1^2 (x^2 + y^2)

Implicit plot

Implicit plot

Alternate form

((x - 1) x + y^2)^2 = x^2 + y^2

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

Expanded form

x^4 - 2 x^3 + 2 x^2 y^2 + x^2 - 2 x y^2 + y^4 = x^2 + y^2

x^4 - 2 x^3 + 2 x^2 y^2 - 2 x y^2 + y^4 - y^2 = 0

Real solutions

x = -1/4, y = -sqrt(3)/4

x = -1/4, y = sqrt(3)/4

Solutions

y = -sqrt(-2 x^2 + 2 x - sqrt(4 x + 1) + 1)/sqrt(2)

y = sqrt(-2 x^2 + 2 x - sqrt(4 x + 1) + 1)/sqrt(2)

y = -sqrt(-x^2 + x + 1/2 sqrt(4 x + 1) + 1/2)

y = sqrt(-x^2 + x + 1/2 sqrt(4 x + 1) + 1/2)

Integer solution

x = 0, y = ± 1

x = 0, y = 0

x = 2, y = 0

Implicit derivatives

(dx(y))/(dy) = -(y + 2 x y - 2 x^2 y - 2 y^3)/(3 x^2 - 2 x^3 + y^2 - 2 x y^2)

(dy(x))/(dx) = -(3 x^2 - 2 x^3 + y^2 - 2 x y^2)/(y + 2 x y - 2 x^2 y - 2 y^3)

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