Q. 84.0( 4 Votes )
Find the equation of the straight line passing through the point of intersection of 2x + y – 1 = 0 and x + 3y – 2 = 0 and making with the coordinate axes a triangle of area 3/8 sq. units.
Answer :
Given:
2x + y – 1 = 0 and x + 3y – 2 = 0
To find:
The equation of the straight line passing through the point of intersection of 2x + y – 1 = 0 and x + 3y – 2 = 0 and making with the coordinate axes a triangle of area 3/8 sq. units.
Explanation:
The equation of the straight line passing through the point of intersection of 2x + y − 1 = 0 and x + 3y − 2 = 0 is given below:
2x + y − 1 + λ (x + 3y − 2) = 0
⇒ (2 + λ)x + (1 + 3λ)y − 1 − 2λ = 0
⇒
So, the points of intersection of this line with the coordinate axes are and
It is given that the required line makes an area of square units with the coordinate axes.
⇒ 3 |3λ2 + 7λ + 2| = 4 |4λ2 + 4λ + 1|
⇒ 9λ2 + 21λ + 6 = 16λ2 + 16λ + 4
⇒ 7λ2 – 5λ – 2 = 0
⇒ λ = 1,
Hence, the equations of the required lines are
3x + 4y – 1 – 2 = 0 and
⇒ 3x + 4y – 3 = 0 and 12x + y – 3 = 0
Rate this question :






















If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point
RD Sharma - MathematicsFind the equation of a straight line passing through the point of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and perpendicular to the straight line x – y + 9 = 0.
RD Sharma - MathematicsFind the equation of a straight line through the point of intersection of the lines 4x – 3y = 0 and 2x – 5y + 3 = 0 and parallel to 4x + 5 y + 6 = 0.
RD Sharma - MathematicsProve that the family of lines represented by x(1 + λ) + y(2 – λ) + 5 = 0, λ being arbitrary, pass through a fixed point. Also, find the fixed point.
RD Sharma - MathematicsFind 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.
RD Sharma - MathematicsFind the equations of the lines through the point of intersection of the lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and whose distance from the origin is.
Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 whose distance from the point (3, 2) is .
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.
RD Sharma - Mathematics