(k+1)x^2-8kx+(3k+5) calculate the value for k
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In the first octant, the given plane forms a triangle with vertices corresponding to the plane's intercepts along each axis.
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, we can parameterize it by
where
and 
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With respect to our parameterization, we have
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Now that we know the vertices of the surface
where
With respect to our parameterization, we have
Since it is a square, the diagonals are congruent. If a square is split like this, it becomes two congruent right triangles. The relationship between the sides and hypotenuse is a 1:
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