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Question

The least distance of the line 8x4y+73=0 from the circle 16x2+16y2+48x8y43=0 is

A
52 units
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B
25 units
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C
35 units
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D
45 units
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Solution

The correct option is B 25 units
For given circle, centre will be (32,14) and radius r=5 units

Now, perpendicular distance from centre to the line 8x4y+73=0 is
d=∣ ∣ ∣ ∣8(32)4(14)+7382+(4)2∣ ∣ ∣ ∣
d=6045=35>r units

So, line lies externally to the circle.
least distance is |dr|=25 units

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