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Grade 11Algebra

Locus of all points P(x,y) satisfying x3 + y3 +3xy =1 consist of union of.....
1) a line and an isolated point
2)a line and an isolated point
3) a line and a circle
4) a circle and an isolated point...
......with proper solutions....

Profile image of Janhavi
7 Years agoGrade 11
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1 Answer

Profile image of Aditya Gupta
7 Years ago
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=0
So x+y-1=0 is obviously a line
And 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

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