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Q.16 Locus all point p(x, y) satisfying ...

Q.16 Locus all point `p(x, y)` satisfying `x^3+y^3+3xy=1` consists of union of (A) a line and an isolated point (B) a line pair and an isolated point C) a line and a circle (D) a circle and an isolated point.

Text Solution

Verified by Experts

Given,
`x^3+y^3+3xy=1`
`x^3+y^3+(−1)^3−3xy(−1)=0`
using the identity
`a^3+b^3+c^3−3abc=(a+b+c)(a^2+b^2+c^2−ab−bc−ca)`
=`(x+y−1)(x^2+y^2+1−xy+y+x)=0`
...
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