Advertisements
Advertisements
Question
The distance between the lines y = mx + c1 and y = mx + c2 is ______.
Options
`(c_1 - c_2)/sqrt(m^2 + 1)`
`|c_1 - c_2|/sqrt(1 + m^2)`
`(c_2 - c_1)/sqrt(1 + m^2)`
0
Advertisements
Solution
The distance between the lines y = mx + c1 and y = mx + c2 is `|c_1 - c_2|/sqrt(1 + m^2)`.
Explanation:
Given equations are y = mx + c1 .....(i)
And y = mx + c2 .....(ii)
Slopes of equation (i) and equation (ii) are same
i.e., m
So, they are parallel lines.
∴ Distance between the two lines = `|c_1 - c_2|/sqrt(1 + m^2)`.
APPEARS IN
RELATED QUESTIONS
Find the points on the x-axis, whose distances from the `x/3 +y/4 = 1` are 4 units.
What are the points on the y-axis whose distance from the line `x/3 + y/4 = 1` is 4 units.
Find perpendicular distance from the origin to the line joining the points (cosΘ, sin Θ) and (cosΦ, sin Φ).
Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x– 7y + 5 = 0 and 3x + y = 0.
Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.
Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.
Find the co-ordinates of the point, which divides the line segment joining the points A(2, − 6, 8) and B(− 1, 3, − 4) externally in the ratio 1 : 3.
Prove that the line y − x + 2 = 0 divides the join of points (3, −1) and (8, 9) in the ratio 2 : 3.
Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle tan−1 \[\left( \frac{5}{12} \right)\] with the positive direction of x-axi .
Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to the line x − 2y = 1.
Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to the line 3x − 4y+ 8 = 0.
Find the equation of a line perpendicular to the line \[\sqrt{3}x - y + 5 = 0\] and at a distance of 3 units from the origin.
Find the distance of the point (4, 5) from the straight line 3x − 5y + 7 = 0.
Find the perpendicular distance of the line joining the points (cos θ, sin θ) and (cos ϕ, sin ϕ) from the origin.
If sum of perpendicular distances of a variable point P (x, y) from the lines x + y − 5 = 0 and 3x − 2y + 7 = 0 is always 10. Show that P must move on a line.
If the length of the perpendicular from the point (1, 1) to the line ax − by + c = 0 be unity, show that \[\frac{1}{c} + \frac{1}{a} - \frac{1}{b} = \frac{c}{2ab}\] .
Determine the distance between the pair of parallel lines:
4x − 3y − 9 = 0 and 4x − 3y − 24 = 0
Determine the distance between the pair of parallel lines:
8x + 15y − 34 = 0 and 8x + 15y + 31 = 0
Determine the distance between the pair of parallel lines:
y = mx + c and y = mx + d
Determine the distance between the pair of parallel lines:
4x + 3y − 11 = 0 and 8x + 6y = 15
Find the equation of two straight lines which are parallel to x + 7y + 2 = 0 and at unit distance from the point (1, −1).
Answer 3:
Prove that the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y= 6.
Find the equations of the lines through the point of intersection of the lines x − y + 1 = 0 and 2x − 3y+ 5 = 0, whose distance from the point(3, 2) is 7/5.
If the centroid of a triangle formed by the points (0, 0), (cos θ, sin θ) and (sin θ, − cos θ) lies on the line y = 2x, then write the value of tan θ.
Write the value of θ ϵ \[\left( 0, \frac{\pi}{2} \right)\] for which area of the triangle formed by points O (0, 0), A (a cos θ, b sin θ) and B (a cos θ, − b sin θ) is maximum.
Write the distance between the lines 4x + 3y − 11 = 0 and 8x + 6y − 15 = 0.
Write the locus of a point the sum of whose distances from the coordinates axes is unity.
The area of a triangle with vertices at (−4, −1), (1, 2) and (4, −3) is
The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.
The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centroid is
The shortest distance between the lines
`bar"r" = (hat"i" + 2hat"j" + hat"k") + lambda (hat"i" - hat"j" + hat"k")` and
`bar"r" = (2hat"i" - hat"j" - hat"k") + mu(2hat"i" + hat"j" + 2hat"k")` is
If the tangent to the curve y = 3x2 - 2x + 1 at a point Pis parallel toy = 4x + 3, the co-ordinates of P are
A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is ______.
If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point.
The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is ______.
The distance of the point (-3, 2, 3) from the line passing through (4, 6, -2) and having direction ratios -1, 2, 3 is ______units.
