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

The equations of the tangents to the hyperbola 3x²-4y²=12 which are parallel to the line 2x+y+7 =0 are

The equations of the tangents to the hyperbola 2x²-3y²=6 which are perpendicular to the line x-2y+5 =0 are

P is a point on x²/a²-y²/b²=1 and A, A’ are the vertices of the conic. If PA, PA’ meet an asymptote at K and L then (KL)²=

If the circle x²+y²=a² intersects the hyperbola xy=c² in four points (x_i, y_i), for i=1,2,3 and 4 then y₁+y₂+y₃+y₄=

The equation of the normal at the positive end of the latus rectum of the hyperbola x²-3y²=144 is