Lines, `L_1 : x + sqrt(13y) = 2, and L_2 : ax + by = 1,` meet at P and enclose an angle of `45^@` betweenthem. Line `L_3:y= sqrt(13x),` also passes through P then

Lines, L_1 :x + sqrt3y=2, and L_2 : ax+by=1 meet at P and enclose an angle of 45° between them. Line L_3 : y=sqrt3x also passes through P then -

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 bisector of the acute angle between L_1 and L_2 intersects L_3 at R Statement - 1 : The ratio PR : PQ equals 2sqrt2 : sqrt5 Statement - 2 : In any triangle , bisector of an angle divides the triangle into two similar triangle

lines L_1:ax+by+c=0 and L_2:lx+my+n=0 intersect at the point P and make a angle theta between each other. find the equation of a line L different from L_2 which passes through P and makes the same angle theta with L_1

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 .

Consider, L_(1) : 2x + 3y + p – 3 = 0 , L_(2) : 2x + 3y + p + 3 = 0 , where p is a real number, and C : x^(2)+y^(2)+6x–10y+30=0 Statement-I : If line L_(1) is a chord of circle C, then line L_(2) is not always a diameter of circle C. and Statement-II : If line L_(1) is a diameter of circle C, then line L_(2) is not a chord of circle C.

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

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 .