Question-216655

Question Number 216655 by abdelsalam last updated on 14/Feb/25

Answered by issac last updated on 14/Feb/25

y^{4} = y^{2} - x^{2}

y^{4} - y^{2} + \frac{1}{4} - \frac{1}{4} = - x^{2}

{(y^{2} - \frac{1}{2})}^{2} = \frac{1}{4} - x^{2}

y^{2} = \frac{1}{2} \pm \sqrt{\frac{1}{4} - x^{2}}

y = \pm \sqrt{\frac{1}{2} \pm \sqrt{\frac{1}{4} - x^{2}}}

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

4 y^{3} \frac{d y}{d x} = 2 y \frac{d y}{d x} - 2 x

(4 y^{3} - 2 y) \frac{d y}{d x} = - 2 x

\frac{d y}{d x} = - \frac{x}{2 y^{3} - y} = 0

2 y^{3} - y \neq 0, x = 0 ∴ x = 0

∴ that Curve haves two Horizental slope

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