Advertisements
Advertisements
प्रश्न
The distance between the lines y = mx + c1 and y = mx + c2 is ______.
पर्याय
`(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
उत्तर
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
संबंधित प्रश्न
Find the distance between parallel lines:
15x + 8y – 34 = 0 and 15x + 8y + 31 = 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.
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 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 (2, 3) from the line 2x − 3y + 9 = 0 measured along a line making an angle of 45° with the x-axis.
Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to a line having slope 3/4.
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 distance of the line 2x + y = 3 from the point (−1, −3) in the direction of the line whose slope is 1.
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 perpendicular distance of the line joining the points (cos θ, sin θ) and (cos ϕ, sin ϕ) 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.
Show that the product of perpendiculars on the line \[\frac{x}{a} \cos \theta + \frac{y}{b} \sin \theta = 1\] from the points \[( \pm \sqrt{a^2 - b^2}, 0) \text { is }b^2 .\]
Find the perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line \[x - \sqrt{3}y + 4 = 0 .\]
What are the points on y-axis whose distance from the line \[\frac{x}{3} + \frac{y}{4} = 1\] is 4 units?
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.
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
Prove that the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y= 6.
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 locus of a point the sum of whose distances from the coordinates axes is unity.
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 line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.
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
A plane passes through (1, - 2, 1) and is perpendicular to two planes 2x - 2y + z = 0 and x - y + 2z = 4. The distance of the plane from the point (1, 2, 2) 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
Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.
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 ______.
Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.
The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.
