Question

Se implicit differentiation to find an equation of the tangent line to the curve at the given point.7x2 + xy + 7y2 = 15, (1, 1) (ellipse)

Answer 1

F'(x, y) = 14x +xydy/dx + 14ydy/dx = 0
(xy+14y)|dy/dx = -14x
dy/dx = -14x /(xy+14y)
dy/dx |(x=1,y=1) : -14(1) / (1+14) = -14/15

using
y-y1=/x-x1 = -14/15
y-1/x-1 = -14/15
15y-15 = -14x+14
15y+14x -15-14=0
14x +15y = 29