Manipal MET2010MathematicsStraight Lines
If the straight line a₁ x+b₁ y+c₁=0 , a₁ x+b₁ y+c₂=0, a₂ x+b₂ y+d₁=0 and a₂ x+b₂ y+d₂=0 are the sides of rhombus, then
Options
- A(a₂^2+b₂^2 ) (c₁-c₂ )^2= (a₁^2+b₁^2 ) (d₁-d₂ )^2
- B(a₁^2+b₁^2 ) |d₁-d₂ |= (a₂^2+b₂^2 ) |c₁-c₂ |
- C(a₂^2+b₂^2 ) (d₁-d₂ )^2= (a₁^2+b₁^2 ) (c₁-c₂ )^2
- D(a₁^2+b₁^2 ) |c₁-c₂ |= (a₂^2+b₂^2 ) |d₁-d₂ |
Correct answer
A. (a₂^2+b₂^2 ) (c₁-c₂ )^2= (a₁^2+b₁^2 ) (d₁-d₂ )^2
Step-by-step solution
Since, given straight lines are the sides of a rhombus. Therefore, distance between the parallel lines a₁ x+b₁ y+c₁=0, a₁ x+b₁ y+c₂=0 and a₂ x+b₂ y+d₁=0, a₂ x+b₂ y+d₂=0 must be equal |c₁-c₂ | a₁^2+b₁^2 = |d₁-d₂ | a₂^2+b₂^2 (a₂^2+b₂^2 ) (c₁-c₂ )^2= (a₁^2+a₁^2 ) (d₁-d₂ )^2