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

Find the equation of a line through the origin which makes an angle of 45^(@) with the positive direction of 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

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 (a) a-2 (b) a+2 (c) 2/(a+2) (d) 2/a

Write down a unit vector in XY - plane making an angle of 30^(@) 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 through the origin makes and angle alpha  ( 0 lt alpha lt (pi)/(4) ) with the positive direction of x-axis. The equation of its diagonal not passing through the origin is

Find the equation of the line which has the length of the perpendicular from origin to the line as 4 units and the perpendicular segment on the line I makes an angle of 120^(@) with the positive direction of x-axis.

A circle of radius 5 units has diameter along the angle bisector of the lines x+y=2 and x-y=2. If the chord of contact from the origin makes an angle of 45^0 with the positive direction of the x-axis, find the equation of the circle.

Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.

A line passes through the points (6,-7,-1)a n d(2,-3,1)dot Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.