Solve x^2 y^2 - 14x - 12y 76 = 0

Solve the equation

Solve for x

Solve for y

x = \frac{7 + 49 + 912 y ^{3}}{y ^{2}} x = \frac{7 - 49 + 912 y ^{3}}{y ^{2}}

Evaluate

x^{2} y^{2} - 14 x - 12 y \times 76 = 0

Multiply the terms

x^{2} y^{2} - 14 x - 912 y = 0

Rewrite the expression

y^{2} x^{2} - 14 x - 912 y = 0

Substitute a= y^{2},b= - 14 and c= - 912 y into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{14 \pm ( - 14 ) ^{2} - 4 y ^{2} ( - 912 y )}{2 y ^{2}}

Simplify the expression

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x = \frac{14 \pm 196 + 3648 y ^{3}}{2 y ^{2}}

Simplify the radical expression

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x = \frac{14 \pm 2 49 + 912 y ^{3}}{2 y ^{2}}

Separate the equation into 2 possible cases

x = \frac{14 + 2 49 + 912 y ^{3}}{2 y ^{2}} x = \frac{14 - 2 49 + 912 y ^{3}}{2 y ^{2}}

Simplify the expression

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x = \frac{7 + 49 + 912 y ^{3}}{y ^{2}} x = \frac{14 - 2 49 + 912 y ^{3}}{2 y ^{2}}

Solution

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x = \frac{7 + 49 + 912 y ^{3}}{y ^{2}} x = \frac{7 - 49 + 912 y ^{3}}{y ^{2}}

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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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r = 0 r = \frac{2 3 7 cos ( θ ) + 456 sin ( θ )}{3 sin ^{2} ( 2 θ )}

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Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = \frac{- x y ^{2} + 7}{x ^{2} y - 456}

Calculate

x^{2} y^{2} - 14 x - 12 y 76 = 0

Simplify the expression

x^{2} y^{2} - 14 x - 912 y = 0

Take the derivative of both sides

\frac{d}{d x} (x^{2} y^{2} - 14 x - 912 y) = \frac{d}{d x} (0)

Calculate the derivative

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2 x y^{2} + 2 x^{2} y \frac{d y}{d x} - 14 - 912 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

2 x y^{2} + 2 x^{2} y \frac{d y}{d x} - 14 - 912 \frac{d y}{d x} = 0

Collect like terms by calculating the sum or difference of their coefficients

2 x y^{2} - 14 + (2 x^{2} y - 912) \frac{d y}{d x} = 0

Move the constant to the right side

(2 x^{2} y - 912) \frac{d y}{d x} = 0 - (2 x y^{2} - 14)

Subtract the terms

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(2 x^{2} y - 912) \frac{d y}{d x} = - 2 x y^{2} + 14

Divide both sides

\frac{( 2 x ^{2} y - 912 ) \frac{d y}{d x}}{2 x ^{2} y - 912} = \frac{- 2 x y ^{2} + 14}{2 x ^{2} y - 912}

Divide the numbers

\frac{d y}{d x} = \frac{- 2 x y ^{2} + 14}{2 x ^{2} y - 912}

Solution

More Steps

\frac{d y}{d x} = \frac{- x y ^{2} + 7}{x ^{2} y - 456}

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