The equation (y^2)/(1+r)-(x^2)/(1-r)=1 ...

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`

Similar Questions

Explore conceptually related problems

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

Let S={(x,y) in R^(2):(y^(2))/(1+r)-(x^(2))/(1-r)=1} , where r ne pm 1 . Then S represents:

The equation of the ellipse whose focus is (1,0) and the directrix is x+ y+1=0 and eccentricity is equal to 1//sqrt(2) is

Find the equation of the ellipse whose focus is (1,0), the directrix is x+y+1=0 and eccentricity is equal to (1)/(sqrt(2))

The eccentricity of the hyperbola (sqrt(2006))/(4) (x^(2) - y^(2))= 1 is

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

The equation of the ellipse whose focus is (1,-1), directrix x-y-3=0 and eccentricity equals (1)/(2) is :

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