Minimum distance to the surface of an ellipsoid

Calculus Level 3

Given the ellipsoid

x 2 1 0 2 + y 2 1 5 2 + z 2 3 0 2 = 1 \dfrac{x^2}{10^2} + \dfrac{y^2}{15^2} + \dfrac{z^2}{30^2} = 1

and the point P = ( 10 , 15 , 30 P = (10, 15, 30 ), determine the minimum distance d d^* from P P to the surface of the ellipsoid. If Q = ( x 1 , y 1 , z 1 ) Q = (x_1, y_1, z_1) is the point on the surface of the ellipsoid that is closest to P P , then submit the value of 100 ( x 1 + y 1 + z 1 + d ) \lfloor 100 (x_1 + y_1 + z_1 + d^* ) \rfloor , where \lfloor \cdot \rfloor is the floor function, for example 2.8 = 2 \lfloor 2.8 \rfloor = 2 .


The answer is 4652.

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