+267 Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.
+15135 Let k be a positive real number and find k, so that the line is tangent to the circle.
\(y=\sqrt{k-x^2}\\ y=-x+3+k\)
\(\color{blue}k\notin \{+\mathbb{R}\}\)
\(y=\sqrt{k-x^2}\\ y=-x+3+k \)
\(y=\sqrt{{\color{blue}1.365}-x^2}\\ y=-x+3\color{blue}-1.365\)
\(\color{blue}k\in \{ \approx 1.365,\ \approx-1.365\}\) determined with graphics.
If +k is replaced by -k in the problem, it is solvable.
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