Expert: Paul Klarreich - 7/7/2010

Question
Find the equations of the tangent line and the normal line to the curve (x^2+y^2)^2 =(x-y)^2 at the point (1, -1) on the curve.

Answer
Questioner:   Ashley
Category:  Advanced Math
Private:  No
 
Subject:  Calculus
Question:  Find the equations of the tangent line and the normal line to the curve (x^2+y^2)^2 =(x-y)^2 at the point (1, -1) on the curve.
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Use implicit differentiation:

If (x^2+y^2)^2 =(x-y)^2. then:

2(x^2+y^2)(2x + 2y y') = 2(x-y)(1 - y')

Now multiply out, then solve for y'.  (The answer will involve x and y.)

Substitute  x =1,  y = -1  to find y', which is your m[tangent line],

and  -1/that is your  m[normal line].

The rest should be routine.  (Some work, yes, but routine.)