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Grade Select GradeAnalytical Geometry

​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-
  1. x + 2y – 5 = 0
  2. 2x = y =0
  3. 3x + 4y + 5 =0
  4. 3x + 4y – 11 =0

Profile image of Bharat Makkar
11 Years agoGrade Select Grade
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3 Answers

Profile image of Himaja
11 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
Profile image of Himaja
11 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
Profile image of Himaja
11 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

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