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

Mar 30, 2018

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

#### Explanation:

We have:

$6 y \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) - 4 x = 0$

$6 y \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = 4 x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{4 x}{6 y}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 x}{3 y}$

Hopefully this helps!