If `L = 2y-x=0` and if the acute angular bisector of `L=0` and x-axis is `L_1=0` and the acute angular bisector of `L= 0 and y - ` axis is `L_2=0` then theangle between `L_1 = 0 and L_2 = 0` is...

Consider the lines L_(1) -=3x-4y+2=0 " and " L_(2)-=3y-4x-5=0. Now, choose the correct statement(s). (a)The line x+y=0 bisects the acute angle between L_(1) "and " L_(2) containing the origin. (b)The line x-y+1=0 bisects the obtuse angle between L_(1) " and " L_(2) not containing the origin. (c)The line x+y+3=0 bisects the obtuse angle between L_(1) " and " L_(2) containing the origin. (d)The line x-y+1=0 bisects the acute angle between L_(1) " and " L_(2) not containing the origin.

If the lines L_1 and L_2 are tangents to 4x^2-4x-24 y+49=0 and are normals for x^2+y^2=72 , then find the slopes of L_1 and L_2dot

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

Let 2a+3b+c=0 ,If x+5y+7=0 and L=0 are angle bisectors of two lines L_(1)=0 and L_(2)=0 such that L=0 is a member in the family of lines ax+by+c=0 Then area of triangle formed by L=0 with coordinate axes is (in sq,units)

The straight line L-=X+Y+1=0 and L_1-=X+2Y+3=0 " are intersectiong, m is the 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 .

The lines L_(1) : y - x = 0 and L_(2) : 2x + y = 0 intersect the line L_(3) : y + 2 = 0 at P and Q respectively . The bisectors of the acute angle between L_(1) and L_(2) intersect L_(3) at R . Statement 1 : The ratio PR : RQ equals 2sqrt2 : sqrt5 Statement - 2 : In any triangle , bisector of an angle divides the triangle into two similar triangles .

The lines L_(1) : y - x = 0 and L_(2) : 2x + y = 0 intersect the line L_(3) : y + 2 = 0 at P and Q respectively . The bisectors of the acute angle between L_(1) and L_(2) intersect L_(3) at R . Statement 1 : The ratio PR : RQ equals 2sqrt2 : sqrt5 Statement - 2 : In any triangle , bisector of an angle divides the triangle into two similar triangles .

Statement I . The combined equation of l_1,l_2 is 3x^2+6xy+2y^2=0 and that of m_1,m_2 is 5x^2+18xy+2y^2=0 . If angle between l_1,m_2 is theta , then angle between l_2,m_1 is theta . Statement II . If the pairs of lines l_1l_2=0,m_1 m_2=0 are equally inclined that angle between l_1 and m_2 = angle between l_2 and m_1 .

Let L be the line x-2y+3=0 .The equation of line L_1 is parallel to L and passing through (1,-2).Find the distance between L and L_1 .