Advertisements
Advertisements
प्रश्न
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 ______.
विकल्प
1 : 2
3 : 7
2 : 3
2 : 5
Advertisements
उत्तर
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 3 : 7.
Explanation:
The given equations are
3x + 4y + 5 = 0 .......(i)
3x + 4y – 5 = 0 .....(ii)
And 3x + 4y + 2 = 0 ......(iii)
Clearly, equation (i), (ii) and (iii) are parallel to each other as the coefficients of x and y are same.
Distance between parallel lines (i) and (iii) we get
`|(5 - 2)/sqrt((3)^2 + (4)^2)| = 3/5` ......`[(because "Distance between two"),("parallel lines" = |("c"_1 - "c"_2)/sqrt("a"^2 + "b"^2)|)]`
Distance between parallel lines (ii) and (iii) we get
`|(-5 - 2)/sqrt((3)^2 + (4)^2)| = 7/5`
∴ Ratio between the distances = `3/5 : 7/5` = 3 : 7
APPEARS IN
संबंधित प्रश्न
Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).
Find the distance between parallel lines l (x + y) + p = 0 and l (x + y) – r = 0
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 distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.
Prove that the line y − x + 2 = 0 divides the join of points (3, −1) and (8, 9) in the ratio 2 : 3.
A line passes through a point A (1, 2) and makes an angle of 60° with the x-axis and intersects the line x + y = 6 at the point P. Find AP.
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 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.
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
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:
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.
Write the locus of a point the sum of whose distances from the coordinates axes is unity.
The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis 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 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
Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.
The distance of the point P(1, – 3) from the line 2y – 3x = 4 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 between the lines y = mx + c1 and y = mx + c2 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:
The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.
The point of intersection of the diagonals of the rectangle whose sides are contained in the lines x = 8, x = 10, y = 11, and y =12 is
