SOLUTION: Find the equations of the tangent line and normal line to the graph of 6x^2-2xy+y^3=9 at the point (2,-3)

Question 554379: Find the equations of the tangent line and normal line to the graph of 6x^2-2xy+y^3=9 at the point (2,-3)
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

6x� - 2xy + y� = 9

Find the derivative implicitly term by term:

12x - 2(x + y) + 3y� = 0

Solve for 

12x - 2x - 2y + 3y� = 0

Isolate the terms in  

-2x + 3y� = -12x + 2y

(-2x + 3y�) = -12x + 2y

 = 

Write the positive terms first

 = 

 =  =  =  =  = 
    
Finding the tangent line is the algebra problem of finding the equation 
of the line through the point (2,-3) with a slope of 

The equation of the tangent line at (2,-3) is

y = x - 

Finding the normal line is the algebra problem of finding the equation 
of the line through the point (2,-3) with a slope of 

The equation of the normal line at (2,-3) is

y = x - 

Edwin

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