Advertisements
Advertisements
प्रश्न
Find the equation of the straight line passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.
Advertisements
उत्तर
The graph of the required line is shown below.
The line which is inclined at an angle of 60° with the positive direction of y-axis makes an angle of 30° with x-axis.
Clearly, the slope of the required line is \[m = \tan {30}^\circ = \frac{1}{\sqrt{3}}\]
So, the equation of the required line having slope \[\frac{1}{\sqrt{3}}\] and passes through the point \[P\left( 3, - 2 \right)\] is
\[y + 2 = \frac{1}{\sqrt{3}}\left( x - 3 \right)\]
\[ \Rightarrow x - \sqrt{3}y - 3 - 2\sqrt{3} = 0\]
Hence, the equation of the required line is \[x - \sqrt{3}y - 3 - 2\sqrt{3} = 0\]
APPEARS IN
संबंधित प्रश्न
Find the equation of the straight line passing through the point (6, 2) and having slope − 3.
Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.
Prove that the perpendicular drawn from the point (4, 1) on the join of (2, −1) and (6, 5) divides it in the ratio 5 : 8.
Find the equation of the straight lines passing through the following pair of point :
(0, −a) and (b, 0)
Find the equation of the straight lines passing through the following pair of point :
(at1, a/t1) and (at2, a/t2)
Find the equations of the medians of a triangle, the coordinates of whose vertices are (−1, 6), (−3, −9) and (5, −8).
Find the equations to the diagonals of the rectangle the equations of whose sides are x = a, x = a', y= b and y = b'.
Find the equation to the straight line cutting off intercepts 3 and 2 from the axes.
Find the equation of the line which passes through the point (− 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.
The straight line through P (x1, y1) inclined at an angle θ with the x-axis meets the line ax + by + c = 0 in Q. Find the length of PQ.
If the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] passes through the point of intersection of the lines x + y = 3 and 2x − 3y = 1 and is parallel to x − y − 6 = 0, find a and b.
Three sides AB, BC and CA of a triangle ABC are 5x − 3y + 2 = 0, x − 3y − 2 = 0 and x + y − 6 = 0 respectively. Find the equation of the altitude through the vertex A.
Find the equation of the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 .
Find the equation of a line passing through the point (2, 3) and parallel to the line 3x − 4y + 5 = 0.
Find the equation of a line drawn perpendicular to the line \[\frac{x}{4} + \frac{y}{6} = 1\] through the point where it meets the y-axis.
Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a cos α, a sin α) and (a cos β, a sin β).
Find the length of the perpendicular from the point (4, −7) to the line joining the origin and the point of intersection of the lines 2x − 3y + 14 = 0 and 5x + 4y − 7 = 0.
Find the equations to the straight lines which pass through the origin and are inclined at an angle of 75° to the straight line \[x + y + \sqrt{3}\left( y - x \right) = a\].
Find the equations of the straight lines passing through (2, −1) and making an angle of 45° with the line 6x + 5y − 8 = 0.
Find the equations of the lines through the point of intersection of the lines x − 3y + 1 = 0 and 2x + 5y − 9 = 0 and whose distance from the origin is \[\sqrt{5}\].
Write the integral values of m for which the x-coordinate of the point of intersection of the lines y = mx + 1 and 3x + 4y = 9 is an integer.
If a, b, c are in G.P. write the area of the triangle formed by the line ax + by + c = 0 with the coordinates axes.
Find the locus of the mid-points of the portion of the line x sinθ+ y cosθ = p intercepted between the axes.
If the point (5, 2) bisects the intercept of a line between the axes, then its equation is
The inclination of the straight line passing through the point (−3, 6) and the mid-point of the line joining the point (4, −5) and (−2, 9) is
Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is `7/5`
The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line `sqrt(3) x + y` = 1 is ______.
Equation of the line passing through the point (a cos3θ, a sin3θ) and perpendicular to the line x sec θ + y cosec θ = a is x cos θ – y sin θ = a sin 2θ.
The straight line 5x + 4y = 0 passes through the point of intersection of the straight lines x + 2y – 10 = 0 and 2x + y + 5 = 0.
The equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0 is equidistant from the points (0, 0) and (8, 34).
