A man is walking on a straight line. The arit | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the equation of the line be $\frac{x}{a} + \frac{y}{b} = 1$,where $a$ and $b$ are the $x$ and $y$ intercepts respectively.The arithmetic mean

Vedclass · Accepted Answer

$B$ only

Vedclass · Answer

(D) Let the equation of the line be $\frac{x}{a} + \frac{y}{b} = 1$,where $a$ and $b$ are the $x$ and $y$ intercepts respectively.The arithmetic mean of the reciprocals of the intercepts is given by $\frac{\frac{1}{a} + \frac{1}{b}}{2} = \frac{1}{4}$.This implies $\frac{1}{a} + \frac{1}{b} = \frac{1}{2}$.Since the line passes through $(x, y)$,we have $\frac{x}{a} + \frac{y}{b} = 1$. If we test the point $(2, 2)$,we get $\frac{2}{a} + \frac{2}{b} = 2(\frac{1}{a} + \frac{1}{b}) = 2(\frac{1}{2}) = 1$.Thus,the line always passes through the point $(2, 2)$.Since stone $B$ is at $(2, 2)$,only stone $B$ is on the path of the man.

$A$ 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. Which of these stones is/are on the path of the man?

Similar Questions

The equations of the lines which cut off an intercept of $-1$ from the $y$-axis and are equally inclined to the axes are

If the coordinates of the points $A$ and $B$ are $(1, 0)$ and $(2, \sqrt{3})$,then the angle made by the line $AB$ with the $x$-axis is .....$^o$.

The points $A(-a, -b)$,$B(0, 0)$,$C(a, b)$,and $D(a^2, ab)$ are

If the $x-$intercept of some line $L$ is double that of the line $3x + 4y = 12$ and the $y-$intercept of $L$ is half that of the same line,then the slope of $L$ is

Reduce the equation $\sqrt{3} x + y - 8 = 0$ into normal form. Find the values of $p$ and $\omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module