<PRE><B>Question 826151</B>
So basically you are trying to find the perpendicular distance (which is the same as the shortest distance) 3x-5y+16=0 is closest to the circle (or (0,0), since the centre of the circle is (0,0))
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By subbing the point (0,0) into the Perpendicular Distance Formula, you get:
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 abs(3(0)-5(0)+16) / sqrt(3^2+5^2)
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which equals to 16/sqrt(34)
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The radius of the circle is root 5. 
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16/sqrt(34) IS BIGGER than root 5. The line is further than the radius from the centre of the circle and therefore does not and cannot intersect the circle at any point.</PRE>