What is the equation of the tangent line which touches the curve of x²y - 2y² + 2y = 0 at (2, 3)

Answer 1

x²y - 2y² + 2y = 0 at (2, 3)

Implicit differentiation for the equation is:

2xy+x²(dy/dx) - 4y(dy/dx) +2(dy/dx) = 0

(dy/dx)(x² -4y +2) = -2xy

dy/dx = -2xy / (x² -4y +2)

at (2,3)

dy/dx = -2•(2•3) / (2² -4(3) +2)

dy/dx = 2 (This is the slope of the tangent line)

Using the point-slope form of linear equation, we have:

y-3 = 2(x-2)