CircleHardBloom L3
Question
The shortest distance from the line $3x + 4y = 25$ to the circle $x^{2} + y^{2} = 6x - 8y$ is equal to:
Options
A.$7/5$
B.$9/5$
C.$11/5$
D.$32/5$
Solution
[Key Concept: Shortest distance from a line to a circle = (perpendicular distance of the centre) $-$ radius.]
Shortest distance $= CD - r$
$$\begin{matrix} & \ = \frac{|9 - 16 - 25|}{5} - 5 \\ & \ = \frac{32}{5} - 5 = \frac{7}{5} \end{matrix}$$
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