Solve 1 y^2 =-3(x - 1)

Identify the conic

Find the standard equation of the parabola

Find the vertex of the parabola

Find the focus of the parabola

y^{2} = - 3 (x - 1)

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Solve for x

Solve for y

x = \frac{- y ^{2} + 3}{3}

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Testing for symmetry about the origin

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 derivative with respect to x

Find the derivative with respect to y

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

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Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = - \frac{9}{4 y ^{3}}

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r = \frac{- 3 cos ( θ ) + 9 + 3 sin ^{2} ( θ )}{2 sin ^{2} ( θ )} r = - \frac{3 cos ( θ ) + 9 + 3 sin ^{2} ( θ )}{2 sin ^{2} ( θ )}

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