Question 1022660
If {{{x^2/4 + y^2/10= 14}}}, then after differentiating implicitly and simplifying, we get

{{{x/2+(y(dy/dx))/5 = 0}}}

Substituting the coordinates of (4,10) into the last equation, we get

{{{4/2+(10(dy/dx))/5 = 0}}}

==> {{{2+ 2(dy/dx) = 0}}}, or {{{dy/dx = -1}}}.

Hence the equation of the tangent line to the ellipse at the point (4,10) is 

y-10 = -(x-4), or 

{{{highlight(x + y = 14)}}}