Advertisements
Advertisements
प्रश्न
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).
Advertisements
उत्तर
Let the given points be A (2, 3) and B (4, −1). Let M be the midpoint of AB.
\[\therefore \text { Coordinates of M }= \left( \frac{2 + 4}{2}, \frac{3 - 1}{2} \right)\]
\[ = \left( 3, 1 \right)\]
The equation of the line parallel to 3x − 4y + 6 = 0 is \[3x - 4y + \lambda = 0\]
This line passes through M (3,1).
\[\therefore 9 - 4 + \lambda = 0\]
\[ \Rightarrow \lambda = - 5\]
Substituting the value of \[\lambda\] in \[3x - 4y + \lambda = 0\],we get
\[3x - 4y - 5 = 0\] ,which is the equation of the required line.
APPEARS IN
संबंधित प्रश्न
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:
Passing through the points (–1, 1) and (2, –4).
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 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.
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).
The perpendicular from the origin to a line meets it at the point (– 2, 9), find the equation of the line.
Point R (h, k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.
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.
Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
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.
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.
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 ______.
