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# Q:-Let a point P(h,k) satisfies the equation x3+y3+3xy=1 , then the locus of point P is a1.Straight line2.Circle3.Parabola4.Hyperbolaplease xplain in details Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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