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The smallest ...

Question

The smallest distance between the circle ${(x - 5)}^{2} + {(y + 3)}^{2} = 1$ and the line $5 x + 12 y - 4 = 0$ , is

A

1/13

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B

2/13

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C

3/15

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D

4/15

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Solution

The correct option is A 2/13
Smallest distance $=$ distance from centre $-$ radius
Smallest distance $= ∣ ∣ ∣ ∣ \frac{5 (5) + 12 (- 3) - 4}{\sqrt{5^{2} + 12^{2}}} ∣ ∣ ∣ ∣ - 1 = \frac{15}{13} - 1 = \frac{2}{13} u n i t s$

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