find the joint equation of pairs of lines parallel to the line 3x+4y=0 and which are at a distance of one unit from the origin
Answers
Given : pairs of lines parallel to the line 3x+4y=0 and which are at a distance of one unit from the origin
To Find : the joint equation of pairs of lines
Solution:
Let say Equation of lines parallel to 3x+4y=0
is 3x + 4y + c = 0
Now line is at a distance of 1 unit from origin
1 = | (3(0) + 4(0) + c ) /(√3² + 4²) |
=> 1 = | c/ 5 |
=> c = ±5
3x + 4y ± 5 = 0
3x + 4y + 5 = 0 and 3x + 4y - 5 = 0
joint equation of pairs of lines = (3x + 4y + 5 )(3x + 4y - 5) = 0
=> 9x² + 16y² + 24xy - 25 = 0
9x² + 16y² + 24xy - 25 = 0 is the joint equation of pairs of lines parallel to the line 3x+4y=0 and which are at a distance of one unit from the origin
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