1.

Trace the curve y2 (x2-1)= 2x-1 with solution​

Answer»

Given  :   Curve y² (x² - 1)  = 2x - 1

To find : Trace the Curve

Solution:

y² (x² - 1)  = 2x - 1

=> y² = (2x - 1)/(x² - 1)

x² - 1 ≠ 0

y = - when 2x - 1 = 0 => x = 1/2

x = 1/2  x = - 1,  1

y²  ≥  0

x < - 1    2x - 1  is - ve  & x² - 1 is + ve   hence y² - ve  so no solution

for x < - 1

for    -1 < x  < 1/2     2x - 1 is - ve & x² - 1 is -  ve hence y² + ve  

so y exist for -1 < x  < 1/2  

for 1/2   < x  < 1   , 2x - 1 is + ve & x² - 1 is -  ve hence y² - ve  so no solution

for 1/2   < x  < 1  

for x > 1    2x - 1 is + ve & x² - 1 is +  ve hence y² + ve  

so y exist for  x > 1

x - Domain

-1 < x  < 1/2    ,  x > 1

Graph is attached

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