Thread: To find coordinate of the point, need help, please

Find the coordinates of the points on the curve X^2 -2xy+2y^2=4 at which the tangent is parallel to x-axis.

Originally Posted by Minwoo

Find the coordinates of the points on the curve X^2 -2xy+2y^2=4 at which the tangent is parallel to x-axis.

Use implicit differentiation to find .
Next solve .

Yes, I found dy/dx is (x-y)/(x-2y), then what is the next step? Thank you

Originally Posted by Minwoo

Yes, I found dy/dx is (x-y)/(x-2y), then what is the next step? Thank you

At what points on the curve is it true that

Sorry, I really dunno

Originally Posted by Minwoo

Sorry, I really dunno

Are you saying that you cannot solve

If you are, then you have no business even trying this problem!

You don't really have to find the derivative explicitely. Going back to your original equation, , implicit differentiation gives . Now, because you are looking for points where y'= 0, put y'= 0 into that equation: . That tells you that y= x. Replace y with x in the original equation, to get an equation in x only and solve that for x.

Thank you for the help