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Question

The vertex of the parabola x2+y22xy4x4y+4=0 is at?

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Solution

For a parabola, dydx=0 at the vertex. Hence,
2x+2ydydx2xdydx2y44dydx=0
2x2y4=0
x=2+y
Putting it back in the equation, we get
(2+y)2+y22y(y+2)4(y+2)4y+4=0
4+4y+y2+y22y24y4y84y+4=0
8y=0
y=0
x=2

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