Advertisements
Advertisements
प्रश्न
Determine the distance between the pair of parallel lines:
8x + 15y − 34 = 0 and 8x + 15y + 31 = 0
उत्तर
The parallel lines are
8x + 15y − 34 = 0 ... (1)
8x + 15y + 31 = 0 ... (2)
Let d be the distance between the given lines.
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).
Find the points on the x-axis, whose distances from the `x/3 +y/4 = 1` are 4 units.
Find the distance between parallel lines l (x + y) + p = 0 and l (x + y) – r = 0
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.
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 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 (3, 5) from the line 2x + 3y = 14 measured parallel to a line having slope 1/2.
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.
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 \[( \pm \sqrt{a^2 - b^2}, 0) \text { is }b^2 .\]
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.
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:
Prove that the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y= 6.
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 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 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
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 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 ______.
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:
