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


Correct option is

y = 2x 

Let the equation of the line through (1, 2) be y – 2 = m(x – 1)  

If P denotes the length of the perpendicular from (3, 1) on this line, then



Then P2 is greatest if and only if s is greatest 






So s is greatest for m = 2

and thus the equation of the required line is y = 2x



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If abc are unequal and different from 1 such that the points  are collinear, then  


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