Question

Select and write the most appropriate answer from the given alternatives in each of the following sub-questions :
The slopes of the lines given by `12x^(2)+bxy-y^(2)=0` differ by 7. Then the value of b is :
A. 2
B. `+-2`
C. `+-1`
D. 1

Answer 1

Correct Answer - C
Comparing the equation
`12x^(2)+bxy-y^(2)=0` with `ax^(2)+2hxy+by^(2)=0`, we get
`a=12,2h=b,b=-1`.
Let `m_(1)andm_(2)` be the slopes of the lines represented by `12x^(2)+bxy-y^(2)=0`.
`thereforem_(1)+m_(2)=(-2h)/(b)=(-b)/(-1)=b`
and `m_(1)m_(2)=(a)/(b)=(12)/(-1)=-12`
`therefore(m_(1)-m_(2))^(2)=(m_(1)+m_(2))^(2)-4m_(1)m_(2)`
`=b^(2)+48` ...(i)
But `|m_(1)-m_(2)|=7`
`therefore(m_(1)-m_(2))^(2)=49` ...(ii)
`therefore` From (i) and (ii),
`b^(2)+48=49`
`b^(2)=1`
`thereforeb=+-1`
Hence,the correct answer from the given alternative is