Advertisements
Advertisements
प्रश्न
Find the distance between parallel lines:
15x + 8y – 34 = 0 and 15x + 8y + 31 = 0
Advertisements
उत्तर
We know that the distance between two parallel lines = `|("C"_1 ∼ "C"_2)/(sqrt("a"^2 + "b"^2))|`
Here, C1 = −34, C2 = 31
a = 15, b = 8
∴ Distance between given parallel lines = `|(-34 - 31)/sqrt(15^2 + 8^2)|`
= `65/sqrt(225 + 64)`
= `65/sqrt(289)`
= `65/17` units
APPEARS IN
संबंधित प्रश्न
If the lines `(x-1)/2=(y+1)/3=(z-1)/4 ` and `(x-3)/1=(y-k)/2=z/1` intersect each other then find value of k
Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).
What are the points on the y-axis whose distance from the line `x/3 + y/4 = 1` is 4 units.
Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.
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.
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 line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with the positive direction of x-axis is 15°.
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 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 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.
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 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?
Show that the path of a moving point such that its distances from two lines 3x − 2y = 5 and 3x + 2y = 5 are equal is a straight 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
The equations of two sides of a square are 5x − 12y − 65 = 0 and 5x − 12y + 26 = 0. Find the area of the square.
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 lines x + ay + a = 0, bx + y + b = 0 and cx + cy + 1 = 0 are concurrent, then write the value of 2abc − ab − bc − ca.
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 area of a triangle with vertices at (−4, −1), (1, 2) and (4, −3) is
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
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 ______.
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 ______.
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 ______.
A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 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 |
A straight line passes through the origin O meet the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment Q in the ratio:
Find the length of the perpendicular drawn from the point P(3, 2, 1) to the line `overliner = (7hati + 7hatj + 6hatk) + λ(-2hati + 2hatj + 3hatk)`
