If the product of the perpendiculars drawn from the point (1,1) on the lines `ax^(2)+2hxy+by^(2)=0` is 1, then

Options

A. `h(a-b)+ab=0`
B. `h(a+b)-ab=0`
C. `h(a+b)+ab=0`
D. `h(a-b)-ab=0`

Answer

C

Explanation

We have,
`|(axx1^(2)+2hxx1xx1+bxx1^(2))/(sqrt((a-b)^(2)+4h^(2)))|`
`rArr" "{(a+b)+2h}^(2)=(a-b)^(2)+4h^(2)`
`rArr" "(a+b)^(2)+4h(a+b)=(a-b)^(2)`
`rArr" "4ab+4h(a+b)=0 rArr 4(a+b)+ab=0`