If the gradient one of the lines `ax^2+2h x y+by^2=0` is twice that of the other, then `h^2`=_______`

Options

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

Answer

C

Explanation

Let m and be the gradients of the lines given by `ax^(2)+2hxy+by^(2)=0`. Then,
`m+2m=(-2h)/(b)and mxx2m=(a)/(b)`
`rArr" "m=-(2h)/(3b)and m^(2)=(a)/(2b)`
`rArr" "(4h^(2))/(9b^(2))=(a)/(2b)=rArr 8h^(2)=9ab`