Advertisements
Advertisements
प्रश्न
Find the equation of the line passing through the intersection of the lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
Advertisements
उत्तर
The point of intersection of lines 2x + y = 5 and x + 3y + 8 = 0 is given by \[\left( \frac{23}{5}, - \frac{21}{5} \right)\]
Now, the slope of the line 3x + 4y = 7 \[\text { or } y = - \frac{3}{4}x + \frac{7}{4}\] is \[- \frac{3}{4}\]
Now, we know that the slopes of two parallel lines are equal.
So, the slope of the required line is \[- \frac{3}{4}\]
Now, the equation of the required line passing through \[\left( \frac{23}{5}, - \frac{21}{5} \right)\] and having slope \[- \frac{3}{4}\] is given by
\[y + \frac{21}{5} = - \frac{3}{4}\left( x - \frac{23}{5} \right)\]
\[ \Rightarrow y + \frac{21}{5} = - \frac{3}{4}x + \frac{69}{20}\]
\[ \Rightarrow y + \frac{3}{4}x = \frac{69}{20} - \frac{21}{5}\]
\[ \Rightarrow 20y + 15x = - 15\]
\[ \Rightarrow 3x + 4y + 3 = 0\]
APPEARS IN
संबंधित प्रश्न
Find the equation of the line parallel to x-axis and having intercept − 2 on y-axis.
Find the equation of the straight line passing through the point (6, 2) and having slope − 3.
Find the equation of the line passing through (0, 0) with slope m.
Find the equation of the straight line which passes through the point (1,2) and makes such an angle with the positive direction of x-axis whose sine is \[\frac{3}{5}\].
Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.
Find the equations to the altitudes of the triangle whose angular points are A (2, −2), B (1, 1) and C (−1, 0).
Find the equation of the line passing through the point (−3, 5) and perpendicular to the line joining (2, 5) and (−3, 6).
Find the equation of the straight lines passing through the following pair of point :
(0, −a) and (b, 0)
Find the equation of the straight lines passing through the following pair of point :
(a, b) and (a + b, a − b)
By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.
The vertices of a quadrilateral are A (−2, 6), B (1, 2), C (10, 4), and D (7, 8). Find the equation of its diagonals.
The length L (in centimeters) 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 milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.
Find the equations to the straight lines which go through the origin and trisect the portion of the straight line 3 x + y = 12 which is intercepted between the axes of coordinates.
Find the equation of the line, which passes through P (1, −7) and meets the axes at A and Brespectively so that 4 AP − 3 BP = 0.
Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
Find the equation of the straight line which passes through the point P (2, 6) and cuts the coordinate axes at the point A and B respectively so that \[\frac{AP}{BP} = \frac{2}{3}\] .
Find the equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on X and Y-axes such that a − b = 2.
Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line 2x + 3y = 6 which is intercepted between the axes.
If the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] passes through the point of intersection of the lines x + y = 3 and 2x − 3y = 1 and is parallel to x − y − 6 = 0, find a and b.
Three sides AB, BC and CA of a triangle ABC are 5x − 3y + 2 = 0, x − 3y − 2 = 0 and x + y − 6 = 0 respectively. Find the equation of the altitude through the vertex A.
Find the equation of a line passing through the point (2, 3) and parallel to the line 3x − 4y + 5 = 0.
Find the equation of a line passing through (3, −2) and perpendicular to the line x − 3y + 5 = 0.
Find the equations of the two straight lines through (1, 2) forming two sides of a square of which 4x+ 7y = 12 is one diagonal.
Find the equation of the straight line drawn through the point of intersection of the lines x + y = 4 and 2x − 3y = 1 and perpendicular to the line cutting off intercepts 5, 6 on the axes.
Find the equation of the straight line which passes through the point of intersection of the lines 3x − y = 5 and x + 3y = 1 and makes equal and positive intercepts on the axes.
Write the area of the triangle formed by the coordinate axes and the line (sec θ − tan θ) x + (sec θ + tan θ) y = 2.
If a, b, c are in G.P. write the area of the triangle formed by the line ax + by + c = 0 with the coordinates axes.
The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 is
Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is `7/5`
Equation of the line passing through the point (a cos3θ, a sin3θ) and perpendicular to the line x sec θ + y cosec θ = a is x cos θ – y sin θ = a sin 2θ.
