# ​Q.  IF  a,b,c ARE IN A.P THEN THE IMAGE OF THE POINT OF INTERSECTION OF THE FAMILY OF LINES ax + by + c=0 IN THE LINE y=0 LIES ON THE LINE- x + 2y – 5 = 0 2x = y =0 3x + 4y + 5 =0 3x + 4y – 11 =0

Himaja
40 Points
9 years ago
Since a,b,c are in AP let a = A - d, b = A, c = A + d
ax+by+c = A( x+ y+ 1) – d(x – 1) = 0
The point of intersection of the given family of lines is the point of intersection of the lines x+y+1=0 and x-1 = 0
And it is ( 1, -2)
Image of this point wrt y = 0 is (1,2).
It lies on the lines 3x+4y-11=0, x + 2y – 5 = 0
Himaja
40 Points
9 years ago
Since a,b,c are in AP let a = A - d, b = A, c = A + d
ax+by+c = A( x+ y+ 1) – d(x – 1) = 0
The point of intersection of the given family of lines is the point of intersection of the lines x+y+1=0 and x-1 = 0
And it is ( 1, -2)
Image of this point wrt y = 0 is (1,2).
It lies on the lines 3x+4y-11=0, x + 2y – 5 = 0
Himaja
40 Points
9 years ago
Since a,b,c are in AP let a = A - d, b = A, c = A + d
ax+by+c = A( x+ y+ 1) – d(x – 1) = 0
The point of intersection of the given family of lines is the point of intersection of the lines x+y+1=0 and x-1 = 0
And it is ( 1, -2)
Image of this point wrt y = 0 is (1,2).
It lies on the lines 3x+4y-11=0, x + 2y – 5 = 0