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Question

Find the equation of tangent and normal to the curve x2+3xy+y2=5 at point (1,1) on it.

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Solution

x2+3xy+y2=5at(1,1)
Taking dydx2x+3y+3xdydx+2ydydx=0dydx(3x+2y)=(2x+3y)dydx=(2x+3y)(3x+2y)dydx(1,1)=(5)5=1
Equation of tangent (x1)=1(y1)x+y2=0
Equation of normal
(x1)=1(y1)x1=y1xy=0

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