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If the radius of the sphere $x^{2}+y^{2}+z^{2}-6 x-8 y+10 z+\lambda=0$ is unity, what is the value of $\lambda ?$
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The correct answer is:
49
Given sphere : $x^{2}+y^{2}+z^{2}-6 x-8 y+10 z+\lambda=0$ Its radius $=1$
$\Rightarrow \sqrt{(-3)^{2}+\left(-4^{2}\right)+(5)^{2}-\lambda}=1$
$\Rightarrow 9+16+25-\lambda=1$
$\therefore \lambda=49$
$\Rightarrow \sqrt{(-3)^{2}+\left(-4^{2}\right)+(5)^{2}-\lambda}=1$
$\Rightarrow 9+16+25-\lambda=1$
$\therefore \lambda=49$
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