Determine `x` so that the line passing through `(3,4) and (x ,5)` makes an angle of `135^0` with the positive direction of the x-axis.

Determine x so that 2 is the slope of the line passing through P(2, 5) and Q(x, 3).

If the equation of the pair of straight lines passing through the point (1,1) , one making an angle theta with the positive direction of the x-axis and the other making the same angle with the positive direction of the y-axis, is x^2-(a+2)x y+y^2+a(x+y-1)=0,a!=2, then the value of sin2theta is

Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin and makes an angle of 30^0 with the positive direction of the x-axis.

The line joining the points (x ,2x)a n d(3,5) makes an obtuse angle with the positive direction of the x-axis. Then find the values of xdot

A straight line passes throught the point (-1,4) and makes an angle 60^(@) with the positive direction of the x- axis . Find the equation of the straight line.

Find the equation of the straight line which pass through the point (3,2) and make an angle of 45^(@) with the positive x axis.

A square of side 'a' lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle alpha (0 < alpha' < pi /4 ) with the positive direction of x-axis. Find the equation of diagonal not passing through the origin ?

Write down a unit vector in XY-plane, making an angle of 30^(@) with the positive direction of x-axis.

Find the distance from the point P(4,1) to the line 4x-y=0 measured along the line making and angle 135^(@) with the positive direction of x-axis.

A square of side a lies above the x-axis and has one vertex at the origin. The side passing throuhg the origin makes an angle alpha (0 lt alpha lt (pi)/(4)) with the positive direction of x-axis. Then the equation of its diagonal not passing through the origin is-