Question

A family of curve S is given by `S -= x^(2) +2xy +y^(2)-4x(1-lambda) - 4y (1+lambda) +4`, then `S = 0` represents
A. pair of straight line `AA lambda in R`
B. straight line for exactly one value of `lambda`
C. parabola `AA lambda in R -{0}`
D. ellipse for three values of `lambda`

Answer 1

Correct Answer - B::C
`S = 0 rArr x^(2) +2xy +y^(2) -4x -4y +4 = 4lambda (y-x)`
`rArr (x+y-2)^(2) = 4 lambda (y-x)`
If `lambda =0`, it represents pair of straight line otherwise parabola.