I know for fact that I got up to z = -2/8x -50/8y here right, and I got 2568/8 a

Question

I know for fact that I got up to z = -2/8x -50/8y here right, and I got 2568/8 as a D value and it's keep telling me that it's worng.
here's the problem.
Consider the surface x^2 + 25y^2 + 4z^2 = 30 P = (1, 1, 1)
the equation of the tangent plane to the surface at the point P is?
help! I know for fact that I got up to z = -2/8x -50/8y here right, and I got 2568/8 as a D value and it's keep telling me that it's worng.
here's the problem.
Consider the surface x^2 + 25y^2 + 4z^2 = 30 P = (1, 1, 1)
the equation of the tangent plane to the surface at the point P is?
help!

Explanation / Answer

Since ?F is perpendiular to F = k at any point, we use the gradient.

Here, let F(x, y, z) = x^2 + 25y^2 + 4z^2 = 30.

Since ?F = <2x, 50y, 8y>, a normal to F at (1, 1, 1) is
?F(1, 1, 1) = <2, 50, 8>.

Hence, the equation of the tangent plane at (1, 1, 1) is
?F(1, 1, 1)

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