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X=y^2

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Calculus
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Type your math problem... x=y^2

Question

Identify the conic

Find the standard equation of the parabola

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Find the vertex of the parabola

Find the focus of the parabola

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y^{2} = x

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Solve the equation

$Solve for y$

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y = x y = - x

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Testing for symmetry

Testing for symmetry about the origin

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Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

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Find the first derivative

$Find the derivative with respect to x$

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$Find the derivative with respect to y$

\frac{d y}{d x} = \frac{1}{2 y}

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Find the second derivative

$Find the second derivative with respect to x$

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$Find the second derivative with respect to y$

\frac{d ^{2} y}{d x ^{2}} = - \frac{1}{4 y ^{3}}

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Rewrite the equation

Rewrite in polar form

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r = 0 r = \frac{cos ( θ )}{sin ^{2} ( θ )}

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Graph

Graph