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Mathematics, 20.03.2020 01:58 stacy99
Find the equations of the tangent plane and normal line at the point (β2, 1, β5) to the ellipsoid x2 4 + y2 + z2 25 = 3. SOLUTION The ellipsoid is the level surface (with k = 3) of the function F(x, y, z) = x2 4 + y2 + z2 25 . Therefore, we have Fx(x, y, z) = Correct: Your answer is correct. Fy(x, y, z) = 2y Fz(x, y, z) = Correct: Your answer is correct. Fx(β2, 1, β5) = -1 Correct: Your answer is correct. Fy(β2, 1, β5) = 2 Fz(β2, 1, β5) = -2/5 Correct: Your answer is correct. . Then this theorem gives the equation of the tangent plane at (β2, 1, β5) as β1(x + 2) + 2(y β 1) β 2/5 Correct: Your answer is correct. (z + 5) = 0 which simplifies to 5x β + 2z + 30 = 0. By this theorem, symmetric equations of the normal line are x + 2 β1 = y β 1 2 = Correct: Your answer is correct.
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Find the equations of the tangent plane and normal line at the point (β2, 1, β5) to the ellipsoid x2...
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