1.

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

Answer»

pair of straight LINE `AA lambda in R`
straight line for exactly one value of `lambda`
parabola `AA lambda in R -{0}`
ellipse for three values of `lambda`

SOLUTION :`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.


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