The value of k if (1, 2) (k, -1) are conjugate points with respect to the ellipse 2x²+3y²=6 is

Pole of the line 2x+3y+4=0 w.r.to the ellipse x²/2+y²/4=1 is

The equation of the normal at a point hose eccentric angle is 3π/2+θ to the ellipse x²/9+y²/4=1 is

If 2x-y+3=0, 4x+ky+3=0 are conjugate with respect to the ellipse 5x²+6y²-15=0 then k=

P(θ) and D(θ+π/2) are two points on the ellipse x²/a²+y²/b²=1. The locus of point of intersection of tangents at P and D to the ellipse is

If the variable line l₁(x-a)+y=0 and l₂(x+a)+y=0 are conjugate lines w. r. to the ellipse x²/a²+y²/b²=1. Then the locus of their point of intersection is

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

If the line lx+my=1 is a normal to the ellipse x²/a²+y²/b²=1 then a²/l²-b²/m²=1

The radius of the circle passing through the foci of the ellipse x²/16+y²/9=1 and having its center at (0, 3) is

If x and y are strictly positive such that x+y =1,then the minimum value of  x log x + y log y is