Thank you for the opportunity to help you with your question!

the normal of the curve at (x,y,z) is

(2x, 6y,1)

which should be parallel to <-8,-12,2>

thus we have

2x/(-8) = 6y/(-12) = 1/2

x = -2, y = -1, z =-((-2)^2+3*(-1)^2) = -7

the point is (-2,-1,-7)

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