Suppose the circle having equation `x^2+y^2=3` intersects the rectangular hyperbola `x y=1` at points `A ,B ,C ,a n dDdot` The equation `x^2+y^2-3+lambda(x y-1)=0,lambda in R ,` represents. a pair of lines through the origin for `lambda=-3` an ellipse through `A ,B ,C ,a n dD` for `lambda=-3` a parabola through `A , B , C ,a n dD` for `lambda=-3` a circle for any `lambda in R`

Options

A. a pair of lines through the origin for `lambda=-3`
B. an ellipse through A, B, C and D for `lambda=-3`
C. a parabola through A, B, C and D for `lambda=-3`
D. a circle for any `lambda in R`

Answer

A

Explanation

For `lambda=-3`, the equation becomes
`x^(2)+y^(2)-3xy=0`
which represents a pair of lines through the origin.