Using derivatives, the equation of the tangent line is: y + 2= -(x + 2)
The equation is:
[tex]y - y_0 = m(x - x_0)[/tex]
In which m is the derivative at point [tex](x_0, y_0)[/tex].
The function is:
[tex]x^2 + y^2 = 8[/tex].
Applying implicit differentiation, the derivative is:
[tex]2x\frac{dx}{dx} + 2y\frac{dy}{dx} = 0[/tex]
[tex]2ym = -2x[/tex]
[tex]m = -\frac{x}{y}[/tex]
We have that x = y = -2, hence m = -1 and the equation is:
y + 2= -(x + 2)
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