Advertisements
Advertisements
प्रश्न
Find the distance between parallel lines l (x + y) + p = 0 and l (x + y) – r = 0
Advertisements
उत्तर
It is known that the distance (d) between parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is
given by d = `(|C_1 - C_2|)/sqrt(A^2 + B^2)`
The given parallel lines are l (x + y) + p = 0 and l (x + y) – r = 0.
lx + ly + p = 0 and lx + ly – r = 0
Here, A = l, B = l, C1 = p, and C2 = –r.
Therefore, the distance between the parallel lines is
`d = (|C_1 - C_2|)/sqrt(A^2 + B^2)` = `(|p + r|)/sqrt(l^2 + l^2)` units
= `(|p + r|)/sqrt(2l^2)` units
= `(|p + r|)/(lsqrt2)` units
= `1/sqrt2|(p + r)/(l)|` units
APPEARS IN
संबंधित प्रश्न
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.
If sum of the 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.
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.
Find the distance of the line 2x + y = 3 from the point (−1, −3) in the direction of the line whose slope is 1.
The perpendicular distance of a line from the origin is 5 units and its slope is − 1. Find the equation of the line.
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.
Show that the perpendiculars let fall from any point on the straight line 2x + 11y − 5 = 0 upon the two straight lines 24x + 7y = 20 and 4x − 3y − 2 = 0 are equal to each other.
Find the distance of the point of intersection of the lines 2x + 3y = 21 and 3x − 4y + 11 = 0 from the line 8x + 6y + 5 = 0.
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:
y = mx + c and y = mx + d
Find the ratio in which the line 3x + 4y + 2 = 0 divides the distance between the line 3x + 4y + 5 = 0 and 3x + 4y − 5 = 0
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.
L is a variable line such that the algebraic sum of the distances of the points (1, 1), (2, 0) and (0, 2) from the line is equal to zero. The line L will always pass through
The distance between the orthocentre and circumcentre of the triangle with vertices (1, 2), (2, 1) and \[\left( \frac{3 + \sqrt{3}}{2}, \frac{3 + \sqrt{3}}{2} \right)\] is
The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis in the ratio
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 ______.
Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is
The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centroid is
The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the line 3x + 4y + 5 = 0 and 3x + 4y − 5 = 0 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 P(α, β) be a point on the line 3x + y = 0 such that the point P and the point Q(1, 1) lie on either side of the line 3x = 4y + 8, then _______.
Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.
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 distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is ______.
The distance between the lines y = mx + c1 and y = mx + c2 is ______.
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 ______.
A point moves so that square of its distance from the point (3, –2) is numerically equal to its distance from the line 5x – 12y = 3. The equation of its locus is ______.
The value of the λ, if the lines (2x + 3y + 4) + λ (6x – y + 12) = 0 are
| Column C1 | Column C2 |
| (a) Parallel to y-axis is | (i) λ = `-3/4` |
| (b) Perpendicular to 7x + y – 4 = 0 is | (ii) λ = `-1/3` |
| (c) Passes through (1, 2) is | (iii) λ = `-17/41` |
| (d) Parallel to x axis is | λ = 3 |
The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.
