SOLUTION: Determine the gradient of the curve {{{ x^2+2xy+2y^2=3 }}} at its y-intercepts.

Algebra ->  Conjunction -> SOLUTION: Determine the gradient of the curve {{{ x^2+2xy+2y^2=3 }}} at its y-intercepts.      Log On


   

Question 898412: Determine the gradient of the curve +x%5E2%2B2xy%2B2y%5E2=3+ at its y-intercepts.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the y-intercepts.
x%5E2%2B2xy%2B2y%5E2=3
x%5E2%2B2x%280%29%2B2%280%29%5E2=3
x%5E2=3
x=sqrt%283%29 and x=-sqrt%283%29
.
.
.
Take the implicit derivative,
2xdx%2B2%28xdy%2Bydx%29%2B4ydy=0
2xdx%2B2xdy%2B2ydx%2B4ydy=0
2xdy%2B4ydy=-%282xdx%2B2ydx%29
%282x%2B4y%29dy=-%282x%2B2y%29dx%0D%0A%7B%7B%7Bdy%2Fdx=-%282x%2B2y%29%2F%282x%2B4y%29
dy%2Fdx=-%28x%2By%29%2F%28x%2B2y%29
So then,
x=sqrt%283%29
y=0
dy%2Fdx=-%28sqrt%283%29%2B0%29%2F%28sqrt%283%29%2B0%29
dy%2Fdx=-1
and
x=-sqrt%283%29
y=0
dy%2Fdx=-%28-sqrt%283%29%2B0%29%2F%28-sqrt%283%29%2B0%29
dy%2Fdx=-1