Q.

The equation of a line through the point 1,2 whose distance from the point 3,1 has the greatest value is

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a

y=2x

b

y=x+1

c

x+2y=5

d

y=3x−1

answer is A.

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Detailed Solution

Obviously, the line through Q is at the greatest distance from point P when it is perpendicular to PQ. Now, the slope of line PQ. Now, the slope of line PQ is mPQ=−1/2. Then the slope of perpendicular line passing through Q is y−2=2x−1or 2x−y=0
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The equation of a line through the point 1,2 whose distance from the point 3,1 has the greatest value is