Math, asked by werewolf9569, 9 months ago

Find the equation of all lines having slope –1 that are tangents to the curve

Answers

Answered by rnath0129
1

Step-by-step explanation:

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Answered by hritiksingh1
14

Step-by-step explanation:

The equation of the given curve is y=

1/x-1,x ≠1

The slope of the tangents to the given curve at any point (x,y) is given by,

dx/dy=-1/(x-1)^2

If the slope of the tangent is −1, then we have:

-1/(x-1)^2=-1

(x-1)^2=1

x-1=±1

x=2,0

When x=0, y=−1 and when x=2,y=1.

Thus, there are two tangents to the given curve with the slope −1. These are passing through the points (0,−1) and (2,1).

∴ The equation of the tangent through (0,−1) is given by,

y−(−1)=−1(x−0)⇒x+y+1=0

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

y−1=−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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