Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y2(y2 − 4) = x2(x2 − 5) (0, −2) (devil's curve)

Step-by-step explanation:

Given that:

at point (0, -2)

Taking the differential from the equation above with respect to x;

Collect like terms

Hence, the slope of the tangent line m can be said to be:

At point (0,-2)

m = 0

So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:

(y - y₁ = m(x - x₁))

y + 2 = 0(x - 0)

y + 2 = 0

y = -2