A curve C has equation $2x^2 + y^2 = 2xy.$ Find the exact value of \( \frac{dy}{dx} \) at the point on C with coordinates (3, 2). - Edexcel - A-Level Maths Pure - Question 5 - 2010 - Paper 6

Rearranging gives:

[ 2y \frac{dy}{dx} - 2x \frac{dy}{dx} = 2y - 4x
]

Factoring out ( \frac{dy}{dx} ):

[ \frac{dy}{dx}(2y - 2x) = 2y - 4x
]

Now, we have:

[ \frac{dy}{dx} = \frac{2y - 4x}{2y - 2x}
]

Now, substituting the coordinates ( (3, 2) ):

[ \frac{dy}{dx} = \frac{2(2) - 4(3)}{2(2) - 2(3)} = \frac{4 - 12}{4 - 6} = \frac{-8}{-2} = 4
]

Thus, the exact value of ( \frac{dy}{dx} ) at the point (3, 2) is 4.