Question

Angles made with x-axis by the two lines through the point  (1, 2) and cutting the line x + y = 4 at a distance  from the point (1, 2) are

Solution

Correct option is

Any line through (1, 2) can be written as   

Where θ is the angle which the line makes with +ve direction of x-axis. Any point on this line is

 this point lies on the line x +y = 4  

  

  

SIMILAR QUESTIONS

Q1

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.

Q2

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

 

Q3

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

Q4

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. 

Q5

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

Q6

Find the coordinates of the orthcentre of the triangle whose vertices are (0, 0), (2, –1) and (–1, 3).

Q7

Find straight lines represented by 6x2 + 13xy + 6y2 + 8x + 7y + 2 = 0 and also find the point of intersection.  

Q8

If abc are all distinct, then the equations (b – c)x + (c – a)y + a – b = 0 and (b3 – c3)x + (c3 – a3)y + a3 – b3 = 0 represent the same line if

Q9

If the pair of lines x2 – 2pxy – y2 = 0 and x2 – 2qxy – y2 = 0 are such that each pair bisects the angle between the other pair, then pq equals  

Q10

If the algebraic sum of the perpendicular distances of a variable line from the points (0, 2), (2, 0) and (1, 1) is zero, then the line always passes through the point