Question 380177
Given the ellipse {{{4x^2 + 9y^2 = 40}}}, if we differentiate with respect to x, we have

{{{8x + 18y(dy/dx) = 0}}}

{{{dy/dx = -8 x/18 y = -4 x/9 y}}}

Therefore the slope at (1, -2) is {{{(-4*1)/(9*-2) = 2/9}}}

Given slope 2/9 and a point (1, -2) we can easily find the y-intercept:

{{{-2 = (2/9)(1) + b}}}
{{{b = -20/9}}}

Thus the equation of the line tangent to the ellipse at (1, -2) is {{{y = (2/9)x - 20/9}}}