Advertisements
Advertisements
प्रश्न
Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).
Advertisements
उत्तर
12(x + 6) = 5(y – 2)
or 12x + 72 = 5y – 10
12x – 5y + 82 = 0
Distance of point (x1, y1) from the line ax + by + c = 0 `(("ax"_1 + "by"_1 + "c"))/sqrt("a"^2 + "b"^2)`
∴ Distance from point (−1, 1) to line 12x − 5y + 8 = 0
d = `(|12 xx (-1) - 5 xx 1 + 8|)/sqrt(12^2 + 5^2)`
= `|(12 - 5 + 82)/(sqrt(144 + 25))|`
= `65/13`
= 5 Units
APPEARS IN
संबंधित प्रश्न
Find the distance between parallel lines:
15x + 8y – 34 = 0 and 15x + 8y + 31 = 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 equation of the line parallel to y-axis and drawn through the point of intersection of the lines x– 7y + 5 = 0 and 3x + y = 0.
Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 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.
Find the co-ordinates of the point, which divides the line segment joining the points A(2, − 6, 8) and B(− 1, 3, − 4) externally in the ratio 1 : 3.
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.
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.
Find the distance of the point (4, 5) from the straight line 3x − 5y + 7 = 0.
What are the points on X-axis whose perpendicular distance from the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] is a ?
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:
y = mx + c and y = mx + d
The equations of two sides of a square are 5x − 12y − 65 = 0 and 5x − 12y + 26 = 0. Find the area of the square.
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
Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is
The value of λ for which the lines 3x + 4y = 5, 5x + 4y = 4 and λx + 4y = 6 meet at a point 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
Show that the locus of the mid-point of the distance between the axes of the variable line x cosα + y sinα = p is `1/x^2 + 1/y^2 = 4/p^2` where p is a constant.
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 point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 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:
The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.
The distance of the point (-3, 2, 3) from the line passing through (4, 6, -2) and having direction ratios -1, 2, 3 is ______units.
