SOLUTION: Find the equation of the tangent line to the curve of x^2 + 3xy + y^2 = 5 at (1,1)

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Question 1049706: Find the equation of the tangent line to the curve of x^2 + 3xy + y^2 = 5 at (1,1)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Implicit Differentiation:
2x%2B3%281%2Ay%2Bx%28dy%2Fdx%29%29%2B2y%2A%28dy%2Fdx%29=0----------used quotient rule
2x%2B3y%2B3x%28dy%2Fdx%29%2B2y%28dy%2Fdx%29=0
%283x%2B2y%29%28dy%2Fdx%29=-2x-3y
highlight%28dy%2Fdx=-%282x%2B3y%29%2F%283x%2B2y%29%29


This rate of change as a slope value at (1,1) is:
-%282%2A1%2B3%2A1%29%2F%283%2A1%2B2%2A1%29
-%285%2F5%29
highlight%28-1%29.


Assumption is that point (1,1) is on the curve given. The equation for line tangent to the curve at (1,1) easily found using the point-slope equation form:
y-1=-1%28x-1%29
y=-x%2B1%2B1
highlight%28y=-x%2B2%29---------in slope-intercept form