If the slope of one of the lines represented by `a x^2+2h x y+b y^2=0` is the square of the other, then `(a+b)/h+(8h^2)/(a b)=` (a) 4 (b) 6 (c) 8 (d) none of these

Options

A. 4
B. 6
C. 8
D. None of these

Answer

2

Explanation

Let m and `m^(2)`be the slopes of the lines represented by
`ax^(2)+2hxy+by^(2)=0`. Then ,
`m+m^(2)=-(2h)/(b)`
and `mm^(2)=(a)/(b)orm^(3)=(a)/(b)`
Now , `(m+m^(2))^(3)=(-(2h)/(b))^(3)`
`:.m^(3)+m^(6)+3mm^(2)(m+m^(2))=-(8h^(3))/(b^(3))`
`:.(a)/(b^(2))(a+b)+(8h^(2))/(b^(3))=(6ah)/(b^(2))`
`:. (a+b)/(h)+(8h^(2))/(ab)=6`
These are the set of parallel lines and the distance between parallel lines are equal . So , the figure is a rhombus.