`x^2/(r^2-r-6)+y^2/(r^2-6r+5)=1` will represent ellipse if r lies in the interval

(x^(2))/(r^(2)+r-6)+(y^(2))/(r^(2)-6r+5)=1 will represent the ellipse if r lies in the interval

x ^(2) (lamda ^(2) - 4 lamda + 3) +y ^(2) (lamda ^(2) - 6 lamda +5) =1 will represent an ellipse if lamda lies in the interval

Equation (x^(2))/(r-2) + (y^(2))/(5-r) = 1 represents an ellipse if

The equatio (x ^(2 ))/( 2 -r) + (y ^(2))/(r -5) +1=0 represents an ellipse, if

The equation (x^(2))/(1-r)-(y^(2))/(1+r)=1,r>1 represents (a)an ellipse (b) a hyperbola (c)a circle (d) none of these

If (1+a)y^(2)-2ay+3>=0AA y in R, then a lies in the interval

The equation (y^2)/(1+r)-(x^2)/(1-r)=1 (a) represents a hyperbola of eccentricity equal to (2)/(sqrt(r+1)) if r in(0,1) (b) represents a hyperbola of eccentricity equal to sqrt((1-r)/(1+r) if rin(0,1) (c) represents a ellipse of eccentricity equal to sqrt((2)/(r+1)) if rgt1 (d) represents a ellipse of eccentricity equal to sqrt((r+1)/(2)) if rgt1

The expression (x^(2)+2x+1)/(x^(2)+2x+7) lies in the interval; (x in R)

If (y^(2)-5y+3)(x^(2)+x+1)<2x for all x in R, then fin the interval in which y lies.