Q:-Let a point P(h,k) satisfies the equation x³+y³+3xy=1 , then the locus of point P is a

1.Straight line

2.Circle

3.Parabola

4.Hyperbola

please xplain in details

Dear Tapasranjan Das

x³+y³+3xy-1=0

(x+y)³ -3xy(x+y) +3xy -1 =0

(x+y)³ -1³ -3xy(x+y-1) =0

(x+y-1)[(x+y)² +1 +(x+y)] --3xy(x+y-1) =0

(x+y-1) [(x+y)² +1 +(x+y) -3xy]=0

(x+y-1) [x²+y² +1 +x+y -xy]=0

 x+y -1 =0 rpresent a straight line

 and for x²+y² +1 +x+y -xy]=0  check value of  Δ

Δ will also come zero so it represent a pair of straight line

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