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