The condition that the line x cos α + y sin α =p to be a tangent to the hyperbola x²/a² -y²/b² =1 is

The equation of conjugate axis of the  hyperbola 5x²-4y²-30x-8y-30=0  is

The equation to the pair of asymptotes of the hyperbola 2x²-y²=1 is

The distance between the foci of the hyperbola x²- 3y²- 4x - 6y - 11 = 0 is

The equation of the normal to the hyperbola x²-4y²= 5  at (3,-1) is

The length of the latus rectum of the hyperbola 9x²-16y²+72x-32y-16=0 is

If the line 3x-y =k is a hyperbola 3x²-y²=3, then k=

The equation of the hyperbola which passes through the point (2,3) and has the asymptotes 4x+3y-7=0 and x-2y-1=0 is

The length of the conjugate axis of the hyperbola 9x²-16y²-18x-64y+89=0 is

The equation of the hyperbola whose eccentricity 2 and foci are the foci of the ellipse x²/25 +y²/9 =1 is