The number of integral values of k for


The number of integral values of $\mathrm{k}$ for which the line, $3 x+4 y=k$ intersects the circle, $x^{2}+y^{2}-2 x-4 y+4=0$ at two distinct points is


Circle $x^{2}+y^{2}-2 x-4 y+4=0$


Centre: $(1,2)$ radius $=1$

line $3 x+4 y-k=0$ intersects the circle at two distinct points.

$\Rightarrow$ distance of centre from the line $<$ radius

$\Rightarrow\left|\frac{3 \times 1+4 \times 2-\mathrm{k}}{\sqrt{3^{2}+4^{2}}}\right|<1$


$\Rightarrow 6<\mathrm{k}<16$

$\Rightarrow \mathrm{k} \in\{7,8,9, \ldots \ldots 15\}$ since $\mathrm{k} \in \mathrm{I}$

Number of $K$ is 9

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