Question

plz solve it
show that the eight point of intersection of the curve
x⁴-5x²y²+4y⁴+x²-y²+x+y+1=0
and its asymptotes lie on the rectangular hyperbola
x²-y²+x+y+1.​

Answer 1

Given :  curve  x⁴-5x²y²+4y⁴+x²-y²+x+y+1=0

rectangular hyperbola  x²-y²+x+y+1.​

Step-by-step explanation:

Draw the curve x⁴-5x²y²+4y⁴+x²-y²+x+y+1=0

using graphing utility

Draw  hyperbola  x²-y²+x+y+1.​

(y - 1/2)² - (x + 1/2)²  =  1

using graphing utility

Observe from the graph   asymptotes lie on the rectangular hyperbola

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