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

Question

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

Answer 1

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