What is the slope of a line tangent to the curve $3 y^{2} - 2 x^{2} = 1$ $3y^2-2x^2=1$ ?

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What is the slope of a line tangent to the curve $3 y^{2} - 2 x^{2} = 1$ $3y^2-2x^2=1$ ?

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Answer 1 · 2018-03-30T16:15:40

The slope of the tangent line is $\frac{2 x}{3 y}$ $(2x)/(3y)$ .

Explanation:

We have:

$6 y (\frac{d y}{d x}) - 4 x = 0$ $6y(dy/dx) - 4x = 0$

$6 y (\frac{d y}{d x}) = 4 x$ $6y(dy/dx) = 4x$

$\frac{d y}{d x} = \frac{4 x}{6 y}$ $dy/dx= (4x)/(6y)$

$\frac{d y}{d x} = \frac{2 x}{3 y}$ $dy/dx = (2x)/(3y)$

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What is the slope of a line tangent to the curve $3 y^{2} - 2 x^{2} = 1$ $3y^2-2x^2=1$ ?

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Explanation:

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What is the slope of a line tangent to the curve $3 y^{2} - 2 x^{2} = 1$ $3y^2-2x^2=1$ ?