Question

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

Solution

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

SIMILAR QUESTIONS

Q1

If sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Q2

If the circumcentre of a triangle lies at the origin and centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and (2a, –2a), then the orthocenter lies on the line.

Q3

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

Q4

If two vertices of a triangle are (–2, 3) and (5, –1), orthocentre lies at the origin and centroid on the line x + y = 7, then the third vertex lies at

Q5

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p andq are the intercepts of the line L on the new axes, then 

                                                          

Q6

If P is a point (xy) on the line, y = –3x such that P and the point (3, 4) are on the opposite sides of the line 3x – 4y = 8, then   

 

Q7

The area enclosed by 2|x| + 3|y≤ 6 is

Q8

Let O be the origin, A (1, 0) and B (0, 1) and P (xy) are points such thatxy > 0 and x + y < 1, then

Q9

If a line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through and angle 15o, then equation of the line is the new position is

Q10

Let 0 < α < π/2 be a fixed angle. If P = (cos θ, sin θ) and Q = (cos (α – θ), sin (α – θ) then Q is obtained from P by