If a hyperbola has one focus at the origin and its eccentricity is 2. One of the directries is x+y+1=0. Then the centre of the hyperbola is

The radius  of  the  auxiliary circle  of  the  hyperbola  x²/12-y²/9=1 is

If a hyperbola has one focus at the origin and its eccentricity is √2. One of the directries is x+y+1=0. Then the equations to its asymptotes are

Radius of the director circle of the hyperbola (x²/81) - (y²/36) = 1 is

The equation of the hyperbola with its axes as coordinate axes, whose transverse axis 8 and eccentricity 3/2 is

The conic represented by 2x²-12xy+23y²-4x-28y-48=0 is

A plane π makes intercepts 3 and 4 respectively on z-axis.If π is parallel to y-axis,then its equation is

If the latus rectum of a hyperbola x²/16-y²/p=1 is 4^1/2. If eccentricity e=

The length of the transverse axis of the hyperbola 4x²-9y²+8x+40=0 is

The locus of the point of intersection of tangents to the  hyperbola  x²-y²=a² which includes an angle of 45⁰ is