If the slope of one of the lines represented by `ax^(2)+2hxy+by^(2)=0` is the square of the other , then `(a+b)/(h)+(8h^(2))/(ab)=`

Options

A. 3
B. 4
C. 5
D. 6

Answer

D

Explanation

Let the slopes be `m,m^2`.
`therefore m+m^2=(-2h)/(b) and mm^2=(a)/(b)rArr m^3((a)/(b))`.
Now , `(m+m^2)^3=(8h^3)/(b^3)`
`rArr m^3+m^6+3m^3(m+m^2)=-(8h^3)/(b^3)`
`rArr (a)/(b)+(a^2)/(b^2)=3(a)/(b)((-2h)/(b))=-(8h^3)/(b^3)`
`rArr (a)/(b)+(a^2)/(b^2)=(6ah)/(b^2)-(8h^2)/(b^3)`
`rArr (ab+a^2)/(b^2)=(6abh-8h^3)/(b^3)`
`rArr ab(a+b)=h(6ab-8h^2)`
`rArr (a+b)/(h)=(6ab-8h^2)/(ab)=6-(8h^2)/(ab)`
`rArr (a+b)/(h)+(8h^2)/(ab)=6`.