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

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

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

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

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

If the equation (4a-3)x^(2)+ay^(2)+6x-2y+2=0 represents a circle,then its centre is a.(3,-1) b.(3,1) c.(-3,1) d.none of these

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

Let A = {1,2,3} and R be a relation on A defind as R = {(1,2), (2,3),(1,3)} , then R is (a) reflexive (b) symmetric (c) transtive (d) none of these

The slopes of the common tanents of the ellipse (x^(2))/(4)+(y^(2))/(1)=1 and the circle x^(2)+y^(2)=3 are +-1(b)+-sqrt(2)(c)+-sqrt(3)(d) none of these

A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on the positive x- and y-axis. If this normal touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then a^2+b^2 is equal to 5 (b) 25 (c) 16 (d) none of these

The sides AC and AB of a o+ABC touch the conjugate hyperbola of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1. If the vertex A lies on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, then the side BC must touch parabola (b) circle hyperbola (d) ellipse