Let `L_1` be a straight line passing through the origin and ` L_2` be the straight line `x + y = 1` if the intercepts made by the circle `x^2 + y^2-x+ 3y = 0` on `L_1` and `L_2` are equal, then which of the following equations can represent `L_1`?

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

Let L be the line 2x+y=2. If the axes are rotated by 45^(@) without transforming the origin ,the intercepts made by line L on the new are

In xy-plane, a straight line L_1 bisects the 1st quadrant and another straight line L_2 trisects the 2nd quadrant being closer to the axis of y . The acute angle between L_1 and L_2 is

A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2x-y-2z=3 .What is the equation of the line L ?

If L_1 and L_2, are the length of the tangent from (0, 5) to the circles x^2 + y^2 + 2x-4=0 and x^2 + y^2-y + 1 = 0 then

A straight line L passing through the point P(-2,-3) cuts the lines, x + 3y = 9 and x+y+1=0 at Q and R respectively. If (PQ) (PR) = 20 then the slope line L can be (A) 4 (B) 1 (C) 2 (D) 3

Let L_(1) and L_(2) be the foollowing straight lines. L_(1): (x-1)/(1)=(y)/(-1)=(z-1)/(3) and L_(2): (x-1)/(-3)=(y)/(-1)=(z-1)/(1) Suppose the striight line L:(x-alpha)/(l)=(y-m)/(m)=(z-gamma)/(-2) lies in the plane containing L_(1) and L_(2) and passes throug the point of intersection of L_(1) and L_(2) if the L bisects the acute angle between the lines L_(1) and L_(2) , then which of the following statements is /are TRUE ?

Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. Which of the following statements are correct? 1. L is a straight line passing through A and in-centre of triangle ABC is on L. 2. L is a straight line passing through A and orthocentre of triangle ABC is a point on L. 3. L is a straight line passing through A and centroid of triangle ABC is a point on L. Select the correct answer using the code given below.

The straight lines L=x+y+1=0 and L_(1)=x+2y+3=0 are intersecting 'm 'me slope of the straight line L_(2) such that L is the bisector of the angle between L_(1) and L_(2). The value of m^(2) is

Line L, perpendicular to the line with equation y = 3x – 5 , contains the point (1, 4). The x-intercepts of L is