Equation of Tangent Line

Question

Find the equation of the tangent line to the following curve at the indicated point.

y² = x²/(xy-4) at (4, 2)

Answer 1

Answer 2

2yy' = [2x(xy - 4) - x²(y + xy')]/(xy - 4)²;

At (4, 2) 4y' = [8(8 - 4) - 16(2 + 4y')]/(8 - 4)²; 4y' = (32 - 32 - 64y')/16; 4y' = - 4y'; 8y' = 0; y' = 0.

Equation of tangent line at (4, 2): y = 2 + 0(x - 4); y = 2.