Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

2x2 + xy + 2y2 = 5, (1, 1)
(ellipse)

Answer 1

Hello :
2x²+xy+2y²=5
Use implicit differentiation : 4x+y+y'x +4yy' =0
x=1 y = 1
4+1+y'+4y' =0
5y' = -5
y' =-1

an equation of the tangent line is : y = -1(x-1)+1
y =-x+2