Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given that: OM = 4 units
∠BAX = 120°
∴ ∠BAO = 180° – 120° or ∠MAO = 60°
∠MOA + MAO = 90° ......[∵ OM ⊥ AB]
θ + 60° = 90°
∴ θ = 30°
So, equation of AB in its normal form
x cos θ + y sin θ = p
⇒ x cos 30° + y sin 30° = 4
⇒ `x xx sqrt(3)/4 + y xx 1/2` = 4
⇒ `sqrt(3)x + y` = 8
Hence, the required equation is `sqrt(3)x + y` = 8
APPEARS IN
संबंधित प्रश्न
The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.
Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is
- Parallel to the x-axis,
- Parallel to the y-axis,
- Passing through the origin.
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 a line passing through the following point:
(−3, 2) and (1, 4)
Find the slope of a line passing through the following point:
\[(a t_1^2 , 2 a t_1 ) \text { and } (a t_2^2 , 2 a t_2 )\]
State whether the two lines in each of the following are parallel, perpendicular or neither.
Through (5, 6) and (2, 3); through (9, −2) and (6, −5)
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).
Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).
What can be said regarding a line if its slope is zero ?
What can be said regarding a line if its slope is negative?
Without using Pythagoras theorem, show that the points A (0, 4), B (1, 2) and C (3, 3) are the vertices of a right angled triangle.
Prove that the points (−4, −1), (−2, −4), (4, 0) and (2, 3) are the vertices of a rectangle.
Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.
A quadrilateral has vertices (4, 1), (1, 7), (−6, 0) and (−1, −9). Show that the mid-points of the sides of this quadrilateral form a parallelogram.
Find the equation of a straight line with slope − 1/3 and y-intercept − 4.
Find the equation of a straight line with slope −2 and intersecting the x-axis at a distance of 3 units to the left of origin.
Find the equation of a line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.
If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).
Find the angles between the following pair of straight lines:
3x + 4y − 7 = 0 and 4x − 3y + 5 = 0
Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
If m1 and m2 are slopes of lines represented by 6x2 - 5xy + y2 = 0, then (m1)3 + (m2)3 = ?
The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.
The intercept cut off by a line from y-axis is twice than that from x-axis, and the line passes through the point (1, 2). The equation of the line is ______.
If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.
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.
P1, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P1, P2 on the bisector of the angle between the given lines.
Slope of a line which cuts off intercepts of equal lengths on the axes is ______.
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.
The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if ______.
