InterviewSolution
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InterviewSolution
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Statement-1: The equation `x^(3)+y^(3)+3xy=1` represents the combined equation of a straight line and a circle. Statement-2: The equation of the straight line contained in `x^(3)+y^(3)+3xy=1` is `x+y=1`A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» Correct Answer - D The equation `x^(3)+y^(3)+3xy=1` can be written as `(x+y)^(2)-3xy(x+y)+3xy-1=0` `rArr {(x+y)^(3)-1^(3)}-3xy(x+y-1)=0` `rArr (x+y-1)(x^(2)+2xy+y^(2)+x+y+1)-3xy(x+y-1)=0` `rArr (x+y-1)(x^(2)+y^(2)-xy+x+y+1)=0` `rArr x+y-1=0, x^(2)+y^(2)-xy+x+y+1=0` Comparing equation `x^(2)+y^(2)-xy+x+y+1=0` with the equation `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0`, we get a=1, b=1, c=1, `h=-(1)/(2), g=(1)/(2), f=(1)/(2)` `:. abc+2fgh-af^(2)-bg^(2)-ch^(2)=1-(1)/(4)-(1)/(4)-(1)/(4)-(1)/(4)=0` So, `x^(2)+y^(2)-xy+x+y+1=0` represents a pair of straight lines. Hence, statement-1 is not true. However, statement-2 is true. |
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