The gradient of one of the lines given by `ax^(2)+2hxy+by^(2)=0` is twice that of the other, then

Options

A. `h^(2)=ab`
B. `h=a+b`
C. `8h^(2)=9ab`
D. `9h^(2)=8ab`

Answer

C

Explanation

Here `m_(1)+m_(2)=-(2h)/b`……….i
and `m_(1)m_(2)=a/b`
Given that `m_(1)=2m_(2)`
On putting the value of `m_(1)` in
Eq. (i) we get
`3m_(2)=-(2h)/b`and `2m_(2)^(2)=a/b`
`implies2(-(2h)/(3b))^(2)=a/b`
`implies8h^(2)=9ab`