Let `L_(1)` be a striaght line passing through the origin and `L_(2)` be the straight `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, find the equation of the line `L_(1)`.

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)?

The bisector of two lines L and L are given by 3x^(2)-8xy-3y^(2)+10x+20y-25=0. If the line L_(1) passes through origin,find the equation of line L_(2).

The line l_(1) passing through the point (1,1) and the l_(2), passes through the point (-1,1) If the difference of the slope of lines is 2. Find the locus of the point of intersection of the l_(1) and l_(2)

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

t_(1),t_(2),t_(3) are lengths of tangents drawn from a point (h,k) to the circles x^(2)+y^(2)=4,x^(2)+y^(2)-4=0andx^(2)+y^(2)-4y=0 respectively further, t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16 . Locus of the point (h,k) consist of a straight line L_(1) and a circle C_(1) passing through origin. A circle C_(2) , which is equal to circle C_(1) is drawn touching the line L_(1) and the circle C_(1) externally. Equation of L_(1) is

L_(1) is a line passing through the point A(n,n+1) having slope, n, L_(2) is a line passing through the point B(-n, n^(2)) and is perpendicular to L_(1) , If L_(1) and L_(2) intersect on y-axis, then n is equal to ________ (n gt 0)

If the lines L_(1) and L_(2) are tangents to 4x^(2)-4x-24y+49=0 and are normals for x^(2)-y^(2)=72, then find the slopes of L_(1) and L_(2).