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anonymous
 one year ago
Given the curve x^2+3xy2y^2=2
Find the equation of the line tangent to the curve at the point (1,1) then Find the coordinates of all other points on this curve with the slope equal to the slope at (1,1)
anonymous
 one year ago
Given the curve x^2+3xy2y^2=2 Find the equation of the line tangent to the curve at the point (1,1) then Find the coordinates of all other points on this curve with the slope equal to the slope at (1,1)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are you okay with implicit differentiation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So did you find dy/dx?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i isolated to yprime and got the slope to be 5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when i plugged in the values.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just do not know what to do with the follow up question.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so I assume you got the tangent line as well then?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, the equation of the tangent was 0=5x4y

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alrighty. So let's see \[\frac{ dy }{ dx } = \frac{ 2x+3y }{ 4y3x }\] And we need all points which also give us a slope of 5. \[5 = \frac{ 2x+3y }{ 4y3x }\] 20y  15x = 2x + 3y 17y = 17x y = x So we can get a slope of 5, whenever y = x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how would we find the fixed point on the curve?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right, we would need to see which of those points actually exist on the curve. Well, we know x must equal to y to get the proper slope. So replace y with x in the original equation.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You'd get x^2 + 3x^2  2x^2 = 2 2x^2 = 2 x = 1 or 1
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