The center of the circle given by r -2 -2 k-15 and - r -2 k-4 isA- 0-1-2B- 1-3-4- -1-3-4D- 0-1-2

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Equation of a Sphere : General Form

The center of...

Question

The center of the circle given by $\to r \cdot (^i + 2^j + 2^k) = 15$ and $| \to r - (^j + 2^k) | = 4$ is

(0, 1, 2)

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(1, 3, 4)

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(- 1, 3, 4)

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(0, - 1, 2)

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Solution

The correct option is B $(1, 3, 4)$
The plane $x + 2 y + 2 z = 15$ cuts the sphere $x^{2} + (y - 1)^{2} + (z - 2)^{2} = 16$ in a circle.
The center of the circle is the foot of perpendicular from the center of the sphere to the given plane. Let $(p, q, r)$ be the foot of perpendicular.

$\frac{p - 0}{1} = \frac{q - 1}{2} = \frac{r - 2}{2} = \frac{- (0 + 2 + 4 - 15)}{9} \Rightarrow (p, q, r) = (1, 3, 4)$

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The center of the circle given by →r⋅(^i+2^j+2^k)=15 and |→r−(^j+2^k)|=4 is

The center of the circle given by $\to r \cdot (^i + 2^j + 2^k) = 15$ and $| \to r - (^j + 2^k) | = 4$ is