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

The conic represented by x²-4x+3y-1=0 is

The locus of poles of tangents to the hyperbola x²-y²=a² w. r. t the parabola y²=4ax is

A normal to the hyperbola x²/a²-y²/b²=1 cuts the axes at K and L. The perpendiculars at K and L axes meet in P. The locus of P is

The equation of the asymptotes of the hyperbola 4x²-9y²=36 are

The sum and product of the slops of the tangents to the hyperbola 2x²-3y²=6 drawn from the point (-1,1) are

The length of latus rectum of parabola y²+8x-2y+17 = 0 is:

If 2x-ky+3=0, 3x-y+1=0 are conjugate lines with respect to 5x²-6y²=15 then k =

The equations of the tangents to the hyperbola 4x²-5y² =20 which make an angle 90⁰ with the transverse axis are