A conic has focus `(1,0)` and corresponding directrix `x + y = 5`. If the eccentricity of the conic is 2, then its equation is

The eccentricity of the conic x ^(2) -4y ^(2) =1 is

The eccentricity of the conic x ^(2) -4y ^(2) =1 is

A conic has latus rectum length 1, focus at (2,3) and the corresponding directrix is x+y -3=0 . Then the conic is

An ellipse with eccentricity e=(1)/(2) has a focus at (0,0) and the corresponding directrix x+6=0 . The equation of the ellipse is

The length of the latus rectum of an ellipse is 4. The focus and its corresponding directrix are (1, -2 ) and 3x + 4y - 15 = 0 then the eccentricity of the ellipse is

If (3,1) is a focus and x=0 is the corresponding directrix of a conic with eccentricity 2, then its vertices are -

An ellipse with the eccentricity e = 1/2 has a focus at (0, 0) and the corresponding directix is x+6=0. The equation of the ellipse is