Question

What is the equation of the tangent line to `y^2(y^2-4)=x^2(x^2-5)` at (0, -2)? Use implicit differentiation.

Answer 1

y=-2

Explanation:

STEP 1 : Simplify the function so that it is easier to be differentiated.
`y^4-4y^2 = x^4-5x^2`

STEP 2 : Use implicit differentiation to differentiate the simplified function.
`4y^3*y'-8y*y'=4x^3-10x`

STEP 3 : Substitute the x- and y-coordinate given into the derivative found.
`4(-2)^3y'-8(-2)y'=0`
`-32y'+16y'=0`
y'=0

STEP 4 : Use the derivative (slope) found and the coordinates to write out the equation of the tangent line.
y+2=0(x-2)
y=-2