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

For a binominal variate X, if n = 4 and P(X = 4) = 6 P(X = 2), then the value of p is:

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