Question

Find the equation of the straight line upon which the length of perpendicular from origin is  units and this perpendicular makes an angle of 75o with the positive direction of x-axis.

Solution

Correct option is

Let AB be the required line and OL be perpendicular to it.  

  

   

∴ equation of line AB will be  

                           

[Normal form]                                                 … (i)  

Now cos 75o = cos (30o + 45o)

                      

  

                          

                        

∴ form (i) equation of line AB is

  

SIMILAR QUESTIONS

Q1

 then the point (x, y) lies on same side of the line 2x + y – 6 = 0 as the point –

Q2

Find the area of the quadrilateral with vertices (3, 3), (1, 4), (–2, 1), (2, –3).

 

Q3

A straight line segment of length ‘p’ moves with its ends on two mutually perpendicular lines. find the locus of the point which divides the line in the ratio 1:2.

Q4

Find the acute angle between the two lines with slopes 1/5 and 3/2.

Q5

If a line has a slope = ½ and passes through (–1, 2); find its equation. 

Q6

If a line has a slope 1/2 and cuts off along the positive y-axis of length 5/2 find the equation of the line.

Q7

If a line passes through two points (1, 5) and (3, 7) find its equation.

Q8

A straight line passes through a point A (1, 2) and makes an angle 60owith the x-axis. This line intersects the line x + y = 6 at the point P. find AP.

Q9

Find the equation of the straight line, which passes through the point (3, 4) and whose intercept on y-axis is twice that on x-axis.

Q10

Find the value of k so that the straight line 2x + 3y + 4 + k (6x – y + 12) = 0 and 7x + 5y – 4 = 0 are perpendicular to each other.