Find The Values Of λ For Which The Point (2 – λ, 1 + 2λ) Lies On The Non-origin Side Of The Line 4x – y – 2 = 0. 

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Question

Find the values of λ for which the point (2 – λ, 1 + 2λ) lies on the non-origin side of the line 4x – y – 2 = 0. 

Solution

Correct option is

λ < 5/6

Since ‘c’ is negative, the expression obtained by putting the coordinates of the point in the equation of line must be positive for the point to lie on non-origin side of the line.  

Testing

SIMILAR QUESTIONS

Q1

Show that the lines 2x – y – 12 = 0 and 3x + y – 8 = 0 intersect at a points which is equidistant from both the coordinates areas.

Q2

Find the area of triangle formed by the lines x – y + 1 = 0, 2x + y + 4 = 0 and x + 3 = 0.  

Q3

The line x + λy – 4 = 0 passes through the point of intersection of 4x – y+ 1 = 0 and x + y + 1 = 0. Find the values of λ.

Q4

Find the equation of a line parallel to x + 2y = 3 and passing through the point (3, 4).

Q5

Find the equation of the line perpendicular to 2x – 3y = 5 and cutting off an intercept 1 on the x-axis

Q6

Find the equation of the straight line passing through (2, –9) and the point of intersection of lines 2x + 5y – 8 = 0,

3x – 4y – 35 = 0  

Q7

Find the equation of straight line passing through the point of intersection of lines 3x – 4y +1 = 0, 5x + y – 1 = 0 and cutting off equal intercepts from coordinate axes.

Q8

Find the distance between the lines 5x + 12y + 40 = 0 and 10x + 24y – 25 = 0.

 

Q9

If P is (1, 2) and the line mirror is 2x – y + 4 = 0, find the coordinates of its image (i.e., Q).

Q10

Find the incentre of ΔABC if A is (4, –2), B is (–2, 4) and C is (5, 5).