Question

Find the equation of all lines having slope −1 that are tangents to the curve  `y = 1/(x -1), x != 1`

Answer 1

∴The equation of the tangent through (2, 1) is given by,

y − 1 = −1 (x − 2)

⇒ y − 1 = − x + 2

⇒ y + x − 3 = 0

Hence, the equations of the required lines are y + x + 1 = 0 and y + x − 3 = 0.