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The equation of a line through the point...

The equation of a line through the point (1, 2) whose distance from the point `(3,1)` has the greatest value is (a)`y=2x` (b)`y=x+1` (c)`x+2y=5` (d) `y=3x-1`

A

y=2x

B

y=x+1

C

x+2y=5

D

y=3x-1

Text Solution

Verified by Experts

The correct Answer is:
A

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 is `m_(PQ) = -1//2`. Then the slope of perpendicular line passing through Q is
y-2 = 2(x-1)
or 2x-y=0
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