Find the equations of the tangent plane and normal line at the point (−2, 1, −5) 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(−2, 1, −5) = -1 Correct: Your answer is correct. Fy(−2, 1, −5) = 2 Fz(−2, 1, −5) = -2/5 Correct: Your answer is correct. . Then this theorem gives the equation of the tangent plane at (−2, 1, −5) as −1(x + 2) + 2(y − 1) − 2/5 Correct: Your answer is correct. (z + 5) = 0 which simplifies to 5x − + 2z + 30 = 0. By this theorem, symmetric equations of the normal line are x + 2 −1 = y − 1 2 = Correct: Your answer is correct.