If the line $3x - 4y - k = 0$ is tangent to the circle $x^2 + y^2 - 4x - 8y + 4 = 0$, then $k$ equals:
Step-by-Step Solution
Key Concept: Centre $(2, 4)$, radius $4$. Distance from $(2, 4)$ to $3x - 4y - k = 0$: $|6 - 16 - k|/5 = 4 \Rightarrow |k + 10| = 20$, giving $k = 10$ or $k = -30$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)