Tangents to x²/a²+y²/b²=1 make an angles θ₁, θ₂ with traverse axis. The equation of the locus of their intersection when cot (θ₁+θ₂)=k is

The polar of (-2, 3) w. r. t the hyperbola 4x²-3y²=12 is

PN is the ordinate of any point P on the hyperbola x²/a² – y²/b² =1. If Q divides AP in the ratio a²:b² then NQ is

The foci of the hyperbola 2x²-y²-4x+4y-10=0 are

If the normal at ‘θ’ on the hyperbola x²/a²-y²/b²=1 meets the tansverse axis at G, the AG, AG’=

The equations to the common tangents to the two hyperbolas x²/a²-y²/b²=1 and y²/a²-x²/b²=1Are

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