Advertisements
Advertisements
प्रश्न
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{2\pi}{3}\]
Advertisements
उत्तर
\[\theta = \frac{2\pi}{3}\]
\[\therefore \text { Slope of the line } = m = \tan\theta\]
\[ \Rightarrow \text { Slope of the line }= \tan\left( \frac{2\pi}{3} \right) = - \tan\left( \frac{\pi}{3} \right) = - \sqrt{3}\]
Hence, the slope of the line is \[- \sqrt{3}\].
APPEARS IN
संबंधित प्रश्न
A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).
Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[- \frac{\pi}{4}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{3\pi}{4}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis: \[\frac{\pi}{3}\]
Find the slope of a line passing through the following point:
(−3, 2) and (1, 4)
Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).
Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: \[\frac{a}{h} + \frac{b}{k} = 1\].
Consider the following population and year graph:
Find the slope of the line AB and using it, find what will be the population in the year 2010.
Without using the distance formula, show that points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
Find the angle between the X-axis and the line joining the points (3, −1) and (4, −2).
Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.
Find the angle between X-axis and the line joining the points (3, −1) and (4, −2).
Find the equation of a straight line with slope − 1/3 and y-intercept − 4.
Find the equation of the strainght line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.
If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.
The line through (h, 3) and (4, 1) intersects the line 7x − 9y − 19 = 0 at right angle. Find the value of h.
Find the angles between the following pair of straight lines:
3x + 4y − 7 = 0 and 4x − 3y + 5 = 0
Find the angles between the following pair of straight lines:
(m2 − mn) y = (mn + n2) x + n3 and (mn + m2) y = (mn − n2) x + m3.
Find the acute angle between the lines 2x − y + 3 = 0 and x + y + 2 = 0.
Show that the line a2x + ay + 1 = 0 is perpendicular to the line x − ay = 1 for all non-zero real values of a.
The angle between the lines 2x − y + 3 = 0 and x + 2y + 3 = 0 is
The reflection of the point (4, −13) about the line 5x + y + 6 = 0 is
Point of the curve y2 = 3(x – 2) at which the normal is parallel to the line 2y + 4x + 5 = 0 is ______.
If one diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is at (1, 2), then find the equation of sides of the square passing through this vertex.
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.
A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are y – 3 = `(2 +- sqrt(3)) (x - 2)`.
The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.
| Column C1 | Column C2 |
| (a) The coordinates of the points P and Q on the line x + 5y = 13 which are at a distance of 2 units from the line 12x – 5y + 26 = 0 are |
(i) (3, 1), (–7, 11) |
| (b) The coordinates of the point on the line x + y = 4, which are at a unit distance from the line 4x + 3y – 10 = 0 are |
(ii) `(- 1/3, 11/3), (4/3, 7/3)` |
| (c) The coordinates of the point on the line joining A (–2, 5) and B (3, 1) such that AP = PQ = QB are |
(iii) `(1, 12/5), (-3, 16/5)` |
The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.
If the line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then the equation of the line in new position is ______.
