The tangent at the point (2, 2) to the curve x²y² - x = 4(1 - y) does not pass through the point. (4, 13), (8, 5), (-2, -2), (-4, -7)

x²y² - x = 4(1 - y)
2xy² + 2y * x² * dy/dx - 1 = -4 * dy/dx
dy/dx(2xy² + 4) = 1 - 2xy²
dy/dx = (1 - 2xy²) / (2xy² + 4)
At (2, 2):
dy/dx|(2,2) = (1 - 2(2)(2²)) / (2(2)(2²) + 4) = (1 - 16) / (16 + 4) = -15 / 20 = -3/4
Equation of tangent: (y - 2) = (-3/4)(x - 2)
4(y - 2) = -3(x - 2)
4y - 8 = -3x + 6
3x + 4y = 14
Let's check which point does not satisfy this equation:
A(4, 13): 3(4) + 4(13) = 12 + 52 = 64 ≠ 14
B(8, 5): 3(8) + 4(5) = 24 + 20 = 44 ≠ 14
C(-2, -2): 3(-2) + 4(-2) = -6 - 8 = -14 ≠ 14
D(-4, -7): 3(-4) + 4(-7) = -12 - 28 = -40 ≠ 14
Only (4, 13) does not satisfy the equation 3x + 4y = 14.