KCET2012MathematicsPair of Lines
If one of the slopes of the pair of lines ax ²+2 hxy + by ²=0 is n times the other, then
Options
- A4(n+1)² a b=n a b
- B4 h²=(n+1)² a b
- C4 nh ²=( n +1)² ab
- D4 a b=(n+1)² h
Correct answer
C. 4 nh ²=( n +1)² ab
Step-by-step solution
Let m be the slope of the lines a x²+2 h x y+b y²=0 , then according to question, other slope will be nm. m + nm = -2 ~h ~b nm ²= a b m = a bn From Eq. (i), we get a b n (1+n)= -2 h b On squaring both sides, we get aligned a bn (1+ n )² &= 4 ~h ² ~b ² 4 ~h ² n &= ab (1+ n )² aligned