Advertisements
Advertisements
Question
Find the angle between the lines x = a and by + c = 0..
Solution
The given lines can be written as
x = a ... (1)
\[y = - \frac{c}{b}\] ... (2)
Lines (1) and (2) are parallel to the y-axis and x-axis, respectively. Thus, they intersect at right angle, i.e. at 90°.
APPEARS IN
RELATED QUESTIONS
Find the equation of the line which satisfy the given condition:
Write the equations for the x and y-axes.
Find the equation of the line which satisfy the given condition:
Passing through the point (–4, 3) with slope `1/2`.
Find the equation of the line which satisfy the given condition:
Passing though (0, 0) with slope m.
Find the equation of the line which satisfy the given condition:
Passing though `(2, 2sqrt3)` and is inclined with the x-axis at an angle of 75°.
Find the equation of the line which satisfy the given condition:
Intersects the x-axis at a distance of 3 units to the left of origin with slope –2.
Find the equation of the line which satisfy the given condition:
Intersects the 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.
Find the equation of the line which is at a perpendicular distance of 5 units from the origin and the angle made by the perpendicular with the positive x-axis is 30°
Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C
P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is `x/a + y/b = 2`
Point R (h, k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.
By using the concept of equation of a line, prove that the three points (3, 0), (–2, –2) and (8, 2) are collinear.
Find the values of q and p, if the equation x cos q + y sinq = p is the normal form of the line `sqrt3 x` + y + 2 = 0.
Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.
Classify the following pair of line as coincident, parallel or intersecting:
2x + y − 1 = 0 and 3x + 2y + 5 = 0
Classify the following pair of line as coincident, parallel or intersecting:
x − y = 0 and 3x − 3y + 5 = 0]
Classify the following pair of line as coincident, parallel or intersecting:
3x + 2y − 4 = 0 and 6x + 4y − 8 = 0.
Prove that the lines \[\sqrt{3}x + y = 0, \sqrt{3}y + x = 0, \sqrt{3}x + y = 1 \text { and } \sqrt{3}y + x = 1\] form a rhombus.
Find the equation to the straight line parallel to 3x − 4y + 6 = 0 and passing through the middle point of the join of points (2, 3) and (4, −1).
Prove that the lines 2x − 3y + 1 = 0, x + y = 3, 2x − 3y = 2 and x + y = 4 form a parallelogram.
Find the equation of the line mid-way between the parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0.
Prove that the area of the parallelogram formed by the lines a1x + b1y + c1 = 0, a1x + b1y+ d1 = 0, a2x + b2y + c2 = 0, a2x + b2y + d2 = 0 is \[\left| \frac{\left( d_1 - c_1 \right)\left( d_2 - c_2 \right)}{a_1 b_2 - a_2 b_1} \right|\] sq. units.
Deduce the condition for these lines to form a rhombus.
Prove that the area of the parallelogram formed by the lines 3x − 4y + a = 0, 3x − 4y + 3a = 0, 4x − 3y− a = 0 and 4x − 3y − 2a = 0 is \[\frac{2}{7} a^2\] sq. units..
Write an equation representing a pair of lines through the point (a, b) and parallel to the coordinate axes.
Three vertices of a parallelogram taken in order are (−1, −6), (2, −5) and (7, 2). The fourth vertex is
Let ABC be a triangle with A(–3, 1) and ∠ACB = θ, 0 < θ < `π/2`. If the equation of the median through B is 2x + y – 3 = 0 and the equation of angle bisector of C is 7x – 4y – 1 = 0, then tan θ is equal to ______.
