A line moves in such a way that the sum of the intercepts made by it on the axes is always c. The locus of the mid- point of its intercept between the axes is (A) `x+y =2c` (B) `x+y=c` (C) `2(x+y)=c` (D) None of these

Options

A. x+y=2c
B. x+y=c
C. 2(x+y)=c
D. 2x+y=c

Answer

C

Explanation

Let the line intersect the axes at A and B.
Let midpoint of AB be P(h,k).
`therefore A(2h,0) " and " B(0,2k)`
So, equation of line in intercept form is
`(x)/(2h) + (y)/(2k) = 1`
Sum of intercepts is constant c.
`therefore 2h+2k=c`
`therefore 2x+2y=c`
This is the required locus of point P.