Advertisements
Advertisements
प्रश्न
The equation of the line with slope −3/2 and which is concurrent with the lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is
विकल्प
3x + 2y − 63 = 0
3x + 2y − 2 = 0
2y − 3x − 2 = 0
none of these
उत्तर
3x + 2y − 2 = 0
Given:
4x + 3y − 7 = 0 ... (1)
8x + 5y − 1 = 0 ... (2)
The equation of the line with slope \[- \frac{3}{2}\] is given below: \[y = - \frac{3}{2}x + c\] \[\Rightarrow \frac{3}{2}x + y - c = 0\] ... (3)
The lines (1), (2) and (3) are concurrent.
\[\therefore \begin{vmatrix}4 & 3 & - 7 \\ 8 & 5 & - 1 \\ \frac{3}{2} & 1 & - c\end{vmatrix} = 0\]
\[ \Rightarrow 4\left( - 5c + 1 \right) - 3\left( - 8c + \frac{3}{2} \right) - 7\left( 8 - \frac{15}{2} \right) = 0\]
\[ \Rightarrow - 20c + 4 + 24c - \frac{9}{2} - 56 + \frac{105}{2} = 0\]
\[ \Rightarrow \frac{- 40c + 8 + 48c - 9 - 112 + 105}{2} = 0\]
\[ \Rightarrow 8c = 8\]
\[ \Rightarrow c = 1\]
On substituting c = 1 in \[y = - \frac{3}{2}x + c\], we get:
\[y = - \frac{3}{2}x + 1\]
\[ \Rightarrow 3x + 2y - 2 = 0\]
APPEARS IN
संबंधित प्रश्न
Find the distance between P (x1, y1) and Q (x2, y2) when :
- PQ is parallel to the y-axis,
- PQ is parallel to the x-axis
Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
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 equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.
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, −5), and (1, 2)
State whether the two lines in each of the following are parallel, perpendicular or neither.
Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)
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).
Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
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.
Without using the distance formula, show that points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
Find the angle between X-axis and the line joining the points (3, −1) and (4, −2).
Find the equation of the strainght line intersecting 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 equations of the altitudes of a ∆ ABC whose vertices are A (1, 4), B (−3, 2) and C (−5, −3).
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 image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
Find the angles between the following pair of straight lines:
3x + y + 12 = 0 and x + 2y − 1 = 0
Find the angles between the following pair of straight lines:
3x − y + 5 = 0 and x − 3y + 1 = 0
Show that the line a2x + ay + 1 = 0 is perpendicular to the line x − ay = 1 for all non-zero real values of a.
Write the coordinates of the image of the point (3, 8) in the line x + 3y − 7 = 0.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
The reflection of the point (4, −13) about the line 5x + y + 6 = 0 is
Find the equation to 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.
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). Find the coordinates of the point A.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are ______.
Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1).
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.
Slope of a line which cuts off intercepts of equal lengths on the axes is ______.
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.
If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.
The points A(– 2, 1), B(0, 5), C(– 1, 2) are collinear.
