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A family of curve S is given by S -= x^(...

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`

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`

Text Solution

Verified by Experts

The correct Answer is:
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.
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Knowledge Check

  • The value of lambda so that the equation lambda x^2+2xy+lambday^2+4x+4y+3=0 represent a pair of straight lines is

    A
    `5/3`
    B
    `5/31`
    C
    1
    D
    none of these

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