Determine whether the lines tangent to the curve at the x-inters of the curve are parallel. ?????

x^2 + xy + y^2 = 27





I found the expression for the slope of the curve at any point (x,y) which is dy/dx = (-2x - y)/(x + 2y) (that was part a)





then is says determine whether the lines tangent to the curve at the x-inters of the curve are parallel. shoe analysis that leads to your conclusion. (part b)


(i got lost here)





the part c: find the points on the curve where the lines tangent to the curve are vertical.





slope of vertical is undefined...so i set the bottom of dy/dx= (-2x - y)/(x + 2y) equal to 0 (then the slope would be undefined)





so i came up with y=-x/2





i put that into the original equation x^2 + xy + y^2 = 27


and got... x^2 - (x^2)/2x + (x^2)/4 = 27





then im lost again











help!!

Determine whether the lines tangent to the curve at the x-inters of the curve are parallel. ?????
dy/dx which you found ... is the slope of the tangent.


now use coordinate geometry to find the equation of the tangent.





lines tangent to the curve at the x intercept of the curve ... we can find this by puttting y=0 in the equation of the curve.


we get


x = sqrt27





the x intercept of the slope is sqrt 27


the POINT is (sqrt 27, 0)








put x=sqrt 27 and y=0 in dy/dx to find dy/dx at (sqrt27,0)





the equation of the tangent will be


y - 0 = dy/dx(at sqrt27,0) (x- sqrt27)

















hope that helped
Reply:Well, I'm no math genious but I'm pretty good at English and I think that whether should be rather. =p



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