Show that the equation `2x^(2) + xy - y^(2) + x + 4y - 3 = 0` represents a pair of lines.

Show that the equation `2x^(2) + xy - y^(2) + x + 4y - 3 = 0` represen

1.	Show that the equation `2x^(2) + xy - y^(2) + x + 4y - 3 = 0` represents a pair of lines.
Answer» Given, `2x^(2)+xy-y^(2)+x+4y-3=0` On comparing it with `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` We get `a=2,h=(1)/(2),b=-1,g=(1)/(2),f=2,c=-0` Consider D `=\|{:(a,h,g),(h,b,f),(g,f,c):}\|` `=\|{:(2,(1)/(2),(1)/(2)),((1)/(2),-1,2),((1)/(2),2,-3):}\|` `=2(3-4)-(1)/(2)(-(3)/(2)-1)+(1)/(2)(1+(1)/(2))` `=-2+(5)/(4)+(3)/(4)=0` Since D=0, the given equation repesents a pair of straight lines.

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Show that the equation `2x^(2) + xy - y^(2) + x + 4y - 3 = 0` represents a pair of lines.

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