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anonymous
 one year ago
The slope of the tangent to a curve at any point (x, y) on the curve is x/y. Find the equation of the curve if the point (2, −2) is on the curve.
anonymous
 one year ago
The slope of the tangent to a curve at any point (x, y) on the curve is x/y. Find the equation of the curve if the point (2, −2) is on the curve.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure how to do this one

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3what do you know about the relation between `slope of tangent line` and `first derivative` ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well the first derivative represents the slope of the tangent line on any point of the function you derive

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3You're given that the `slope of tangent line` equals x/y, so setup an equation using that info

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i thought that x/y was the derivative

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes \[\dfrac{dy}{dx}=\dfrac{x}{y}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what do i solve for though ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3thats the equation ^

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you need to solve the curve \(y\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so implicit differentiation ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3An usual algebraic equation involves isolating a "variable", but a differential equation involves solving for a "curve"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3familiar with variable separation ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay im getting \[\sqrt{C  x^2}\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3looks partially correct, show me ur work

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439277292623:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this drawing tool is dreadful

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3leave it as \[y^2=x^2+C\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439277527370:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Now plugin the initial condition, \((2, 2)\), and solve \(C\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1439277677058:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439277671100:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1439277771874:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh woops , my mind was slipping

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so know we just plug that into dw:1439277880677:dw right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0these area my answer choices by the way x + y = 0 x2 − y2 = −2 x2 + y2 = 16 x2 + y2 = 8 i assume its D

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[y^2=x^2+C\] plugin \((2, 2)\) \[(2)^2=2^2+C\implies C = 8\] so the solution is \[y^2=x^2+8\] which is same as \[x^2+y^2=8\]
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