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  4. If 3 x+y+k=0 is a tangent to the circle x2+y2=10, then the values of k are

Q. If $3 x+y+k=0$ is a tangent to the circle $x^{2}+y^{2}=10$, then the values of $k$ are

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Solution:

$3 x +y +k=0\, \&\, x^{2}+y^{2}=10$
$y=-3 x-k\,\, a^{2}=10$
$m=-3\, \&\, c=-k$
$\therefore c^{2}=a^{2}\left(m^{2}+1\right)$
$ k^{2}=10(9+1)=100$
$\therefore k=\pm 10$

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