A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of the line on the coordinate axes is 1 4 .  Three stones A, B and C are placed at the point (1, 1), (2, 2) and (4, 4) respectively. Then which of these stones is / are on the path of the man?

Option 1 -

A only

Option 2 -

All the three     

Option 3 -

C only

Option 4 -

B only

0 3 Views | Posted 2 weeks ago
Asked by Shiksha User

  • 1 Answer

  • V

    Answered by

    Vishal Baghel | Contributor-Level 10

    2 weeks ago
    Correct Option - 3


    Detailed Solution:

    According to question,

    1 2 ( 1 a + 1 b ) = 1 4

    1 a + 1 b = 1 2 . . . . . . . . ( i )

    Equation of required line is x a + y b = 1

    Obviously B (2, 2) satisfying condition (i)

Similar Questions for you

A
alok kumar singh

Eqn : y – 0 = tan45° (x – 9) Þ y = (x – 9)

Option (B) is correct

A
alok kumar singh

|r1 – r2| < c1c2 < r1 + r2

-> | 2 4 λ 2 9 | < | 2 λ | < 2 + 4 λ 2 9

| 2 λ | 2 < 4 λ 2 9    

4 λ 2 + 4 8 | λ | < 4 λ 2 9

  λ > 1 3 8 , λ < 1 3 8           

4 λ 2 9 > 0

λ > 3 2 , λ < 3 2

λ ( , 1 3 8 ) ( 1 3 8 , )           

Now,

| 2 4 λ 2 9 | < | 2 λ |            

4 + 4 λ 2 9 4 4 λ 2 9 < 4 λ 2  

4 4 λ 2 9 > 5 λ R  

λ ( , 1 3 8 ) ( 1 3 8 , )  

A
alok kumar singh

(y – 2) = m (x – 8)

⇒   x-intercept

⇒     ( 2 m + 8 )

⇒   y-intercept

⇒   (–8m + 2)

⇒   OA + OB = 2 m 2  + 8 – 8m + 2

f ' ( m ) = 2 m 2 8 = 0  

-> m 2 = 1 4

-> m = 1 2

-> f ( 1 2 ) = 1 8

->Minimum = 18

V
Vishal Baghel

Kindly consider the following figure

A
alok kumar singh

  h = c o s θ + 3 2          

k = s i n θ + 2 2            

-> c o s θ = 2 h 3 & s i n θ = 2 k 2

-> ( h 3 / 2 ) 2 + ( k 1 ) 2 = 1 4

circle of radius r = 1 2  

 

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