Respuesta :
Answer:
slope = - [tex]\frac{\sqrt{3} }{3}[/tex]
Step-by-step explanation:
Differentiating implicitly with respect to x
2x + 2y [tex]\frac{dy}{dx}[/tex] = 0
2y [tex]\frac{dy}{dx}[/tex] = - 2x
[tex]\frac{dy}{dx}[/tex] = - [tex]\frac{2x}{2y}[/tex] = - [tex]\frac{x}{y}[/tex]
[tex]\frac{dy}{dx}[/tex] is the measure of the slope of the tangent
rearrange equation to find corresponding y-coordinate of x = - 2
y² = 16 - 4 = 12 = 2[tex]\sqrt{3}[/tex] ⇒ y = ± 2[tex]\sqrt{3}[/tex]
using x = - 2, y = - 2[tex]\sqrt{3}[/tex], then
[tex]\frac{dy}{dx}[/tex] = - [tex]\frac{1}{\sqrt{3} }[/tex] = - [tex]\frac{\sqrt{3} }{3}[/tex]
