Question

A straight line through the point (1, 1) meets the x-axis at 'A' and the y-axis at 'B'. The locus of the mid-point of AB is

• A. 2xy+ x + y = 0
• B. x + y – 2xy = 0
• C. x + y + 2 = 0
• D. x + y – 2 = 0

Answer 1

Answer: (B)

x + y – 2xy = 0

Answer 2

AM = BM

Eq. of line AB is

y – 1 = m (x – 1) …..(i)

Put x = 0 Ž y = (1 – m)

Put y = 0 Ž x =

Let mid point of AB be M (h, k).

So, $\mathrm { h } = \frac { 0 + \left( 1 - \frac { 1 } { \mathrm {~m} } \right) } { 2 }$ ….(i)

$\mathrm { k } = \frac { 0 + ( 1 - \mathrm { m } ) } { 2 }$ …..(ii)

By (ii) & (iii) Ž Eliminate (m)

So, h + k – 2hk = 0

\ Locus of point M is x + y – 2xy = 0