If `(1)/(2)|x|=1 and |y|=x+1`, then `y^(2)` could be

If 2x = 2y + 1 , then which of the following could be true?

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

If y=(x^(2)+x+1)/(x^(2)-x+1)," then "(x^(2)-x+1)^(2)y_(1)=

The locus of the middle point of the chord of the circle x ^(2) + y ^(2) = a ^(2) such that the chords passes through a given point (x _(1) , y _(1)), is : a) x ^(2) + y ^(2) - x x _(1) - y y _(1) =0 b) x ^(2) + y ^(2) = x _(1) ^(2) + y _(1) ^(2) c) x + y = x _(2) + y _(1) d) x + y = x _(1) ^(2) + y _(1) ^(2)

If the point x_(1)+t(x_(2)-x_(1)), y_(1)+t(y_(2)-y_(1)) divides the join of (x_(1), y_(1)) and (x_(2), y_(2)) internally then

If the point x_(1)+t(x_(2)-x_(1)),y_(1)+t(y_(2)-y_(1)) divides the join of (x_(1),y_(1)) and (x_(2),y_(2)) internally then locus of t is