A man is walking on a straight line- The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 1-4- Three stones A- B and C are placed at the points 1- 1- 2- 2 and 4- 4 respectively- Then which of these stones is-are on the path of the man-

xa+yb=1 ha+kb=1…(y) nbsp; and 1/a+1/b2=14 ∴1a+1b=12… (2) From (1) and (2) Line passes through fixed point B(2,2) ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to be on the Same Plane

A man is walk...

Question

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

B

only

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A

only

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the three

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C

only

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Solution

The correct option is A $B$ only

$\frac{x}{a} + \frac{y}{b} = 1$
$\frac{h}{a} + \frac{k}{b} = 1 \dots (y)$
and $\frac{\frac{1}{a} + \frac{1}{b}}{2} = \frac{1}{4}$
$∴ \frac{1}{a} + \frac{1}{b} = \frac{1}{2} \dots (2)$
From $(1)$ and $(2)$
Line passes through fixed point $B (2, 2)$

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A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 14. Three stones A,B and C are placed at the points (1,1),(2,2) and (4,4) respectively. Then which of these stones is/are on the path of the man?

The correct option is A B only xa+yb=1 ha+kb=1…(y) and 1a+1b2=14 ∴1a+1b=12…(2) From (1) and (2) Line passes through fixed point B(2,2)

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

The correct option is A $B$ only

$\frac{x}{a} + \frac{y}{b} = 1$
$\frac{h}{a} + \frac{k}{b} = 1 \dots (y)$
and $\frac{\frac{1}{a} + \frac{1}{b}}{2} = \frac{1}{4}$
$∴ \frac{1}{a} + \frac{1}{b} = \frac{1}{2} \dots (2)$
From $(1)$ and $(2)$
Line passes through fixed point $B (2, 2)$