x^2 -2xy + y^2 - 8x + 4y + 20 = 0
2x - 2y - 2xy' + 2yy' - 8 + 4y' = 0
(-2x+2y+4)y' = -2x+2y+8
y' = (x-y-4)/(x-y-2)
So, y'=0 when x-y-4 = 0
y' is undefined when x-y-2 = 0
To find the points, intersect the lines with the parabola
Use implicit differentiation to find the points where the parabola defined by
x^{2}-2xy+y^{2}-8x+4y+20 = 0
has horizontal and vertical tangent lines.
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