Question 767187: 3x^2+xy+3y^2=7; (1,1) Write the equation for the tangent line in slope-intercept form.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 3x^2+xy+3y^2=7; (1,1) Write the equation for the tangent line in slope-intercept form.
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Do you mean tangent at the point (1,1)?
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3x^2+xy+3y^2=7
Differentiate implicitly
6x*dx + y*dx + x*dy + 6y*dy = 0
(6x + y)dx + (x + 6y)dy = 0
dy/dx = -(6x+y)/(6y+x)
@(1,1) = -1
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m = -1
y = mx + b
1 = -1*1 + b
b = 2
--> y = -x + 2
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