Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + 2xy − y2 + x = 11, (4, 9) (hyperbola)

Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

x² + 2xy − y² + x = 11,  (4, 9)

 (hyperbola)

Answer 1

x² + 2xy - y² + x = 11

2x + 2x(dy/dx) + 2y - 2y(dy/dx) + 1 = 0

At the point (4,9), we have 8 + 8(dy/dx) + 18 - 18(dy/dx) + 1 = 0

-10(dy/dx) = -27

dy/dx = 27/10= slope of tangent line

equation of tangent line: y - 9 = (27/10)(x - 4)