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
Advertisements
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
Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.
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
A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).
If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`
Find the slope of a line passing through the following point:
(−3, 2) and (1, 4)
What can be said regarding a line if its slope is positive ?
What can be said regarding a line if its slope is negative?
By using the concept of slope, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
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 2 and y-intercept 3 .
Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.
Show that the perpendicular bisectors of the sides of a triangle are concurrent.
Find the equations of the altitudes of a ∆ ABC whose vertices are A (1, 4), B (−3, 2) and C (−5, −3).
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 θ is the angle which the straight line joining the points (x1, y1) and (x2, y2) subtends at the origin, prove that \[\tan \theta = \frac{x_2 y_1 - x_1 y_2}{x_1 x_2 + y_1 y_2}\text { and } \cos \theta = \frac{x_1 x_2 + y_1 y_2}{\sqrt{{x_1}^2 + {y_1}^2}\sqrt{{x_2}^2 + {y_2}^2}}\].
If two opposite vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.
The angle between the lines 2x − y + 3 = 0 and x + 2y + 3 = 0 is
The medians AD and BE of a triangle with vertices A (0, b), B (0, 0) and C (a, 0) are perpendicular to each other, if
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
The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.
Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.
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.
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 ______.
The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.
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.
Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).
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 ______.
Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.
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 ______.
The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.
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.
The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are y – 3 = `(2 +- sqrt(3)) (x - 2)`.
The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.
