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

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The equation of the given curve is .

The slope of the tangents to the given curve at any point is given by, 



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









When , and when

Thus, there are two tangents to the given curve with the slope . These are passing through the points and

 The equation of the tangent through is given by,



And equation of the tangent through is given by, 

  



Hence, the equations of the required lines are and
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Question Text
Find the equation of all lines having slope -1 that are tangents to the curve  .
Answer TypeText solution:1
Upvotes150