Find the locus of a point which moves at a un | vedclass

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(A) Let the moving point be $P(x, y, z)$.Given that the distance of point $P$ from the fixed point $C(1, -2, 2)$ is $1$.Using the distance formula,we

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$x^2 + y^2 + z^2 - 2x + 4y - 4z + 8 = 0$

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(A) Let the moving point be $P(x, y, z)$.Given that the distance of point $P$ from the fixed point $C(1, -2, 2)$ is $1$.Using the distance formula,we have $\sqrt{(x - 1)^2 + (y + 2)^2 + (z - 2)^2} = 1$.Squaring both sides,we get $(x - 1)^2 + (y + 2)^2 + (z - 2)^2 = 1^2$.Expanding the squares: $(x^2 - 2x + 1) + (y^2 + 4y + 4) + (z^2 - 4z + 4) = 1$.Simplifying the equation: $x^2 + y^2 + z^2 - 2x + 4y - 4z + 9 = 1$.Subtracting $1$ from both sides: $x^2 + y^2 + z^2 - 2x + 4y - 4z + 8 = 0$.

Find the locus of a point which moves at a unit distance from the point $(1, -2, 2)$.

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