Question

if a variable line passes through the point of intersection of lines x+2y-1=0 and 2x-y-1=0 and meets the coordinate axes in A and B ,then the locus of the mid point of AB is ??

Answer 1

Answer:

x−10xy+3y=0

Step-by-step explanation:

The point of intersection of the two given lines is (35,15).

Let the mid point of AB be (x,y). So we have

A=(2x,0)

B=(0,2y)

Using the intercept form for the variable line and substituting (35,15) in it we have,

(35)2x+(15)2y=1

Or in simpler terms, the locus of the midpoint of AB is a hyperbola given by

x−10xy+3y=0