A line `L_1-=3y-2x-6=0` is rotated about its point of intersection with the y-axis in the clockwise direction to make it `L_2` such that the are formed by `L_1,L_2` the x-axis, and line `x=5` is `(49)/3s qdotu n i t s` if its point of intersection with `x=5` lies below the x-axis. Find the equation of `L_2dot`

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

A line intersects x-axis at point (-2, 0) and cuts off an intercept of 3 units from the positive side of y-axis. Find the equation of the line.

The lines L_1: x-2y+6=0&L_2: x-2y-9=0 are tangents to the same circle. If the point of contact of L_1 with the circle is (-2,2), then: the centre of the circle is (-7/2,5) the centre of the circle is (-1/2,-1) area of the circle is (45pi)/4s qdotu n t i s the point of contact of L_2 with the circle has the co-ordinates (-5,8)

Lying in the plane x+y+z=6 is a line L passing through (1, 2, 3) and perpendicular to the line of intersection of planes x+y+z=6 and 2x-y+z=4 , then the equation of L is

A straight line L through the point (3,-2) is inclined at an angle 60^@ to the line sqrt(3)x+y=1 . If L also intersects the x-axis then find the equation of L .

The equation of line l_(1) is y=2x+3 , and the equation of line l_(2) is y=2x-5.

Let L be the line 2x+y-2=0 . The axes are rotated by 45^@ in clockwise direction then the intercepts made by the line L on the new axes are respectively

The point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 is

The plane l x+m y=0 is rotated through an angle alpha about its line of intersection with the plane z=0 . Prove that the equation of the plane in its new position is l x+m ypm(sqrt(l^2+m^2)tanalpha)z=0.

A straight line L through the point (3,-2) is inclined at an angle 60^@ to the line sqrt(3)x+y=1 If L also intersects the x-axis then the equation of L is