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The line parallel to x axis and passing through the intersection of lines ax + 2by + 3 b =0 and bx - 2a y - 3 = 0 where(a,b)not equals to 0is A) above x axis at the distance of 3/2 from it B) above x-axis at the distance of 2 by 3it C) below the x-axis of the distance of 2 by 3 from it D below the x-axis at the distance of 3/2 from it

The line parallel to x axis and passing through the intersection of lines ax + 2by + 3 b =0 and bx - 2a y - 3 = 0 where(a,b)not equals to 0is 
A) above x axis at the distance of  3/2 from it
B) above x-axis at the distance of 2 by 3it 
C) below the x-axis of the distance of 2 by 3 from it
D below the x-axis at the distance of 3/2 from it

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear student
 
 
The given lines are ax + 2by + 3b = 0 and bx – 2ay – 3a = 0.
Then the required equation is of the form
ax + 2by + 3b + l(bx – 2ay – 3a) = 0.
(a + bl)x + (2b – 2al)y + (3b-3a) = 0
Since, the lline is given to be parallel to x-axis, hence we must have the coefficient of x to be zero.
Hence, a+bl = 0
l = -a/b
So, the given equation reduces to (2b + 2a2/b)y + (3b + 3a2/b) = 0
This yields 2y + 3 = 0, which is a line parallel to x-axis and since, y = -3/2, so it lies below the x-axis at a distnce of 3/2 from the origin.
 
Regards
Arun

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