If x + y + k = 0 is a tangent to the circle $x^{2} + y^{2}$ - 2x - 4y + 3 = 0 then k =

\pm

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–1, – 5

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Solution

The correct option is B –1, – 5
Radius = Distance from the centre C(1, 2) to x + y + k = 0
$\Rightarrow$ $\sqrt{1 + 4 - 3}$ = $\frac{| 1 + 2 + k |}{\sqrt{2}}$ $\Rightarrow$ $| k + 3 |$ = 2 $\Rightarrow$ k + 3 = $\pm$ 2 $\Rightarrow$ k = -1, - 5

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