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The distance between the parallel lines 3x + 4y + 13 = 0 and 3x + 4y – 13 = 0 is
- a)26
- b)26/3
- c)26/4
- d)26/5
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The distance between the parallel lines 3x + 4y + 13 = 0 and 3x + 4y &...
Given parallel lines3x +4y+13=0
perp length from origin P1= 13/√(3)2 +(4)2
=13/5
and another line 3x+4y-13=0 P2= -13/√(3)2+(4)2
=-13/5
Now distance b/w parallel lines
D=P1-P2
=13/5+13/5
=26/5 units
perp length from origin P1= 13/√(3)2 +(4)2
=13/5
and another line 3x+4y-13=0 P2= -13/√(3)2+(4)2
=-13/5
Now distance b/w parallel lines
D=P1-P2
=13/5+13/5
=26/5 units
Most Upvoted Answer
The distance between the parallel lines 3x + 4y + 13 = 0 and 3x + 4y &...
Given lines:
1) 3x + 4y + 13 = 0
2) 3x + 4y + 13 = 0
To find the distance between these parallel lines, we need to find the perpendicular distance between them.
Step 1: Convert the given lines into slope-intercept form
1) 3x + 4y + 13 = 0
4y = -3x - 13
y = (-3/4)x - 13/4
2) 3x + 4y + 13 = 0
4y = -3x - 13
y = (-3/4)x - 13/4
Step 2: Find the slope of the lines
Both lines have the same slope, which is -3/4.
Step 3: Use the formula for the distance between two parallel lines
The distance between two parallel lines with slopes m1 and m2 is given by:
Distance = |c1 - c2| / sqrt(m1^2 + m2^2)
In this case, m1 = m2 = -3/4 and c1 = 13/4, c2 = 13/4.
Step 4: Calculate the distance
Distance = |13/4 - 13/4| / sqrt((-3/4)^2 + (-3/4)^2)
= 0 / sqrt(9/16 + 9/16)
= 0 / sqrt(18/16)
= 0 / (sqrt(18) / sqrt(16))
= 0 / (sqrt(18) / 4)
= 0
Therefore, the distance between the parallel lines is 0.
1) 3x + 4y + 13 = 0
2) 3x + 4y + 13 = 0
To find the distance between these parallel lines, we need to find the perpendicular distance between them.
Step 1: Convert the given lines into slope-intercept form
1) 3x + 4y + 13 = 0
4y = -3x - 13
y = (-3/4)x - 13/4
2) 3x + 4y + 13 = 0
4y = -3x - 13
y = (-3/4)x - 13/4
Step 2: Find the slope of the lines
Both lines have the same slope, which is -3/4.
Step 3: Use the formula for the distance between two parallel lines
The distance between two parallel lines with slopes m1 and m2 is given by:
Distance = |c1 - c2| / sqrt(m1^2 + m2^2)
In this case, m1 = m2 = -3/4 and c1 = 13/4, c2 = 13/4.
Step 4: Calculate the distance
Distance = |13/4 - 13/4| / sqrt((-3/4)^2 + (-3/4)^2)
= 0 / sqrt(9/16 + 9/16)
= 0 / sqrt(18/16)
= 0 / (sqrt(18) / sqrt(16))
= 0 / (sqrt(18) / 4)
= 0
Therefore, the distance between the parallel lines is 0.
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The distance between the parallel lines 3x + 4y + 13 = 0 and 3x + 4y – 13 = 0 isa)26b)26/3c)26/4d)26/5Correct answer is option 'D'. Can you explain this answer?
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