Advertisements
Advertisements
प्रश्न
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.
उत्तर
The point located at a distance of 2 units on the y-axis from the origin will be (0, 2). The line makes an angle of 30° with the positive direction of the x-axis.
∴ m = tan 30° = `1/sqrt3`
equation of line,
y – y1 = m (x – x1)
y – 2 = `1/sqrt3 ("x" - 0)`
or `sqrt3"y" - 2sqrt3 = "x"`
or `"x" - sqrt3"y" + 2 sqrt3 = 0`
APPEARS IN
संबंधित प्रश्न
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:
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:
Passing through the points (–1, 1) and (2, –4).
Find the equation of the line which satisfy the given condition:
The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.
The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.
Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).
Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
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
The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?
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 area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.
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 2x − 3y + 1 = 0, x + y = 3, 2x − 3y = 2 and x + y = 4 form a parallelogram.
Find the angle between the lines x = a and by + c = 0..
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..
Show that the diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n' = 0, mx + ly + n = 0 and mx + ly + n' = 0 include an angle π/2.
Show that the point (3, −5) lies between the parallel lines 2x + 3y − 7 = 0 and 2x + 3y + 12 = 0 and find the equation of lines through (3, −5) cutting the above lines at an angle of 45°.
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 ______.
