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Grade: 11
`        Locus of all points  P(x,y) satisfying  x3 + y3 +3xy =1 consist of union of..... 1) a line and an isolated point2)a line and an isolated point3) a line and a circle 4) a circle and an isolated point... ......with proper solutions.... `
9 months ago

## Answers : (1)

Aditya Gupta
1672 Points
```							The equation is x^3+y^3+(-1)^3-3xy(-1)=0(x+y-1)((x-y)^2+(y+1)^2+(x+1)^2)/2=0So x+y-1=0 is obviously a lineAnd the rest of the term will be zero only when x-y=0, y+1=0 and x+1=0 or at the point (-1,-1), which is itself an isolated point.So option 2 is correct
```
9 months ago
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