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Find the equations of the tangent plane and normal line at the point (−2, 1, 3) to the ellipsoid

* The level equations * find the equations of the tangent plane and normal line at the point (−2, 1, 3) to the ellipsoid (x ^ 2/4) + and ^ 2 +(z^2/9) = 3

1voto

Ojete chulete Points 0
(x ^ 2/4) + and ^ 2 +(z^2/9) = 3; at the point (- 2; 1; 3) ∂/∂x = x/2; the point: - 1; ∂/∂y = 2y; the point: 2; ∂/∂z = (2/9) z; in point: (2/3) ▼ < (x/2; 2 (2/9) z >;) ▼(-2;1;3) = < - 1; 2; (2/3) > normal straight: (x 1, y1, z1) = (- 2; 1; 3) + t < - 1; 2; (2/3) >; o x = - 2-t; and = 1 +2t; z = 3 +(2/3) t. Tangent plane: (- 1) (x+2) + 2(y-1) + (2/3) (z-3) = 0; -x-2 +2y-2 + (2/3) z - 2 = 0; I multiply by 3: - 3 x-6 +6y-6 + 2z - 6 = 0; -3 x +6y +2z = 18

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