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Find the equation of the tangent line to the curve at the point (0,1):

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Find the equation of the tangent line to the curve x2-xy+y2=y at the point (0,1):

asked Jun 22, 2013 in CALCULUS by skylar Apprentice

1 Answer

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The given equation of the tangent line to the curve x2-xy+y2= y at the point (0,1)

differentiating  on each side

2x - y - x(dy/dx) +2y(dy/dx) = dy/dx

When x = 0 and y = 1

2(0) - 1 - 0(dy/dx) +2(1)dy/dx = dy/dx

-1+2dy/dx - dy/dx = 0

dy/dx = 1

Hence the equation of tangent line

( y -y1) = m (x - x1)

(y - 1) = 1(x - 0)

y - 1 = x

y = x +1

The tangent line of the curve is  y = x+1

 

answered Jun 22, 2013 by goushi Pupil

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