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Find the equation of all lines having slope −1 that are tangents to the curve 
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Asked by Abinaya Last Modified
Answer 
Harshit Bhardwaj
The equation of the given curve is.
The slope of the tangents to the given curve at any point (x, y) is given by,
If the slope of the tangent is −1, then we have:
When x = 0, y = −1 and when x = 2, y = 1.
Thus, there are two tangents to the given curve having slope −1. These are passing through the points (0, −1) and (2, 1).
∴The equation of the tangent through (0, −1) is given by,
∴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.
read less Mayank Dadarwal
Step 1. Differentiate curve Y=1/(x-1)
Step 2. dy/dx is slope of tangent at general point on curve which you find in step 1
Step 3 it is given that slope of tangent is -1 and equal to dy/dx(comes from step 2).
Step4 Now you will values of x put it in equation of curve to get points.
Step 5. Now you are having slope of line and point so you can find equation of tangent.
Be careful while taking square root step4 consider both case with positive and negative.
read less
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