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

The curve represented by x=a(cosh θ+sinh θ), y=b(cosh θ-sinh θ) is

The equation to hyperbola whose centre is (0,0) distance between the foci is 18 and between the directrices is 8 is

The locus of poles of tangents to the circle x²+y²=a²-b² w. r. t the hyperbola x²/a²-y²/b²=1is

If α and β are two points on the hyperbola x²/a²-y²/b²=1 and the chord joining these two points passes through the focus (ae, 0) then e cos α-β/2=

The foot of the normal 3x+4y=7 to the hyperbola 4x²-3y²=1 is