Question

请问这两题高数题怎么做

请问这两题高数题怎么做如图

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Answer 1

9. x ± 2√ (y^2+z^2) = 4, 4(y^2+z^2) = (4-x)^2
8. 球半径 R = 10，球心 C(3, -2, 1)到平面 2x-2y-z+9 = 0 的距离
d = [2*3-2(-2)-1*1+9]/√(2^2+2^2+1^2) = 6,
平面截球的小圆半径 r = √(10^2 - 6^2) = 8
记小圆圆心 A(a, b, 2a-2b+9), 则向量 CA = (a-3, b+2, 2a-2b+8) 与平面法向量平行，
(a-3)/2 = (b+2)/(-2) = (2a-2b+8)/(-1) = t
a = 2t+3, b = -2t-2, 2(2t+3)-2(-2t-2)+8 = -t, t = -2
a = -1, b = 2, 2a-2b+9 = 3， 则 A(-1, 2, 3)