Home
Class 11
MATHS
The straight line a(1)x+b(1)y+c(1)=0 and...

The straight line `a_(1)x+b_(1)y+c_(1)=0 anda_(2)x+b_(2)y+c_(2)=0` are parallel to each other if -

A

`(a_(1))/(a_(2))ne(b_(1))/(b_(2))`

B

`(a_(1))/(b_(1))ne(b_(2))/(a_(2))`

C

`(a_(1))/(a_(2))=(b_(1))/(b_(2))`

D

`(a_(1))/(b_(1))=(b_(2))/(a_(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    CHHAYA PUBLICATION|Exercise EXERCISE 2B (Very Short Answer Type Questions )|16 Videos
  • STRAIGHT LINE

    CHHAYA PUBLICATION|Exercise EXERCISE 2B (Short Answer Type Questions )|23 Videos
  • STRAIGHT LINE

    CHHAYA PUBLICATION|Exercise EXERCISE 2A (Long Answer Type Questions )|19 Videos
  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos

Similar Questions

Explore conceptually related problems

Show that two lines a_(1)x + b_(1) y+ c_(1) = 0 " and " a_(2)x + b_(2) y + c_(2) = 0 " where " b_(1) , b_(2) ne 0 are : (i) Parallel if a_(1)/b_(1) = a_(2)/b_(2) , and (ii) Perpendicular if a_(1) a_(2) + b_(1) b_(2) = 0 .

If the simultaneous linear equations a_(1)x+b_(1)y+c_(1)=0 " and " a_(2)x+b_(2)y+c_(2)=0 have only one solution, then the required condition is -

If the straight lines a_(1)x+b_(1)y+c=0,a_(2)x+b_(2)y+c=0anda_(3)x+b_(3)y+c=0[cne0] are concurrent , show that the points (a_(1),b_(1),(a_(2),b_(2))and(a_(3),b_(3)) are collinear.

Statement - I: Equation of bisectors of the angles between the liens x=0 and y=0 are y=+-x Statement - II : Equation of the bisectors of the angles between the lines a_(1)x+b_(1)y+c_(1)=0anda_(2)x+b_(2)y+c_(2)=0 are (a_(1)x+b_(1)y+c_(1))/(sqrt(a_(1)^(2)+b_(1)^(2)))=+-(a_(2)x+b_(2)y+c_(2))/(sqrt(a_(2)^(2)+b_(2)^(2))) (Provided a_(1)b_(2)nea_(2)b_(1)andc_(1),c_(2)gt0)

Show that the equation of the straight line throught (alpha,beta) and through the point of intersection of the lines a_(1)x+b_(1)y+c_(1)=0 anda_(2)x+b_(2)y+c_(2)=0 is (a_(1)x+b_(1)y+c_(1))/(a_(1)alpha+b_(1)beta+c_(1))=(a_(2)x+b_(2)y+c_(2))/(a_(2)alpha+b_(2)beta+c_(2))

If the two lines a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0 cut the co-ordinates axes in concyclic points. Prove that a_1a_2 = b_1b_2

If the straight lines 2x-3y+5=0andpx+2y=6 be parallel to each other , state which of the following is the value of p ,

If the lines x=a_(1)y+b_(1),z=c_(1)y+d_(1) and x=a_(2)y+b_(2),z=c_(2)y+d_(2) are perpendicular, prove that, 1+a_(1)a_(2)+c_(1)c_(2)=0 .

The straight lines (x)/(a_(1))=(y)/(b_(1))=(z)/(c_(1)) and (x-2)/(a_(2))=(y-3)/(b_(2))=(z)/(c_(2)) will be parallel if -

Represent the following equations in matrix form: a_(1)x+b_(1)y+c_(1)=0 a_(2)x+b_(2)y+c_(2)=0