Home
Class 11
MATHS
Find the equation of the bisector of the...

Find the equation of the bisector of the obtuse angle between the lines `3x-4y+7=0` and `12 x+5y-2=0.`

A

(a) 21x + 77y - 101 = 0

B

(b) 99x - 27y + 81 = 0

C

(c) 21x - 77y + 101 = 0

D

(d) None of the above

Text Solution

Verified by Experts

Firstly, make the constant terms `(c_(1), c_(2))` positive.
3x-4y+7 = 0
and -12x-5y+2=0
`therefore a_(1)a_(2) + b_(1)b_(2) = (3)(-12) + (-4)(-5)`
=-36+20=-16
Hence, "-" sign gives the obtuse bisector.
Therefore, the obtuse bisector is
`((3x-4y+7))/(sqrt((3)^(2) + (-4)^(2))) = ((-12x-5y+2))/(sqrt((-12)^(2) + (-5)^(2)))`
or 13(3x-4y+7) = -5(-12x-5y+2)
or 21x+77y-101 =0
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the equations of the bisector of the acute angle between the lines 3x + 4y + 2 = 0 and 5x + 12y - 5 = 0 .

Find the equation of the bisectors of the anglebetween the lines 4x+3y=5 and x +2y+3=0.

The equation of the line which bisects the obtuse angle between the line x-2y+4=0 and 4x-3y+2=0 is

The equation of the bisector of the acute angle between the lines 2x-y+4=0 and x-2y=1 is (a) x-y+5=0 (b) x-y+1=0 (c) x-y=5 (d) none of these

Find the equations of the bisectors of the angles between the planes 2x-y+2z+3=0a n d3x-2y+6z+8=0 and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.

Find the equations of the bisectors of the angles between the planes 2x-y+2z+3=0a n d3x-2y+6z+8=0 and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.

For the straight lines 4x+3y-6=0 and 5x+12 y+9=0, find the equation of the bisector of the obtuse angle between them, bisector of the acute angle between them, and bisector of the angle which contains (1, 2)

Find the equation of the bisectors of the angles between the lines joining the origin to the point of intersection of the straight line x-y=2 with the curve 5x^2+11 x y-8y^2+8x-4y+12=0

The angle between the line 3x-2y=0 and 2x+3y+5=0 is ………………….. .

The angle between the lines 2x - y+3 = 0 and x + 2y + 3 = 0 is