A point moves such that the sum of the square | vedclass

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(C) Let the two given points be $A(a, 0, 0)$ and $B(-a, 0, 0)$ in a $3D$ coordinate system. Let the moving point be $P(x, y, z)$.According to the prob

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$A$ sphere

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(C) Let the two given points be $A(a, 0, 0)$ and $B(-a, 0, 0)$ in a $3D$ coordinate system. Let the moving point be $P(x, y, z)$.According to the problem,$PA^2 + PB^2 = k$,where $k$ is a constant.$(x-a)^2 + y^2 + z^2 + (x+a)^2 + y^2 + z^2 = k$$(x^2 - 2ax + a^2 + y^2 + z^2) + (x^2 + 2ax + a^2 + y^2 + z^2) = k$$2x^2 + 2y^2 + 2z^2 + 2a^2 = k$$x^2 + y^2 + z^2 = \frac{k - 2a^2}{2}$This equation represents a sphere with its center at the origin $(0, 0, 0)$.

$A$ point moves such that the sum of the squares of its distances from two given points remains constant. The locus of the point is

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