If `a/sqrt(b c)-2=sqrt(b/c)+sqrt(c/b),` where `a , b , c >0,` then the family of lines `sqrt(a)x+sqrt(b)y+sqrt(c)=0` passes though the fixed point given by (a)`(1,1)` (b) `(1,-2)` (c)`(-1,2)` (d) `(-1,1)`

Options

A. (1,1)
B. (1,-2)
C. (-1,2)
D. (-1,1)

Answer

D

Explanation

`(a)/(sqrt(bc))-2 = sqrt((b)/(c)) + sqrt((c)/(b))`
`"or " a=b+c+2sqrt(bc)`
`"or " a=(sqrt(b)+sqrt(c))^(2)`
`"or " (sqrt(a)-sqrt(b)-sqrt(c))(sqrt(a)+sqrt(b)+sqrt(c))=0`
`"or " sqrt(a)-sqrt(b)-sqrt(c)=0`
`"since " sqrt(a)+sqrt(b)+sqrt(c)ne0 " " ("as "a,b,c gt 0).`
`"Comparing with " sqrt(a)x+sqrt(b)y+sqrt(c)=0, " we have "x=-1, y=1`