The equation of the auxiliary circle of x²/12+y²/18=1 is

If the chord of contact of the point (1, -2) with respect to the ellipse 4x²+5y²=20 is ax+by+c=0 then the ascending order  of a, b, c is

The locus of a point P for which the chord of contact of  x²/a²+y²/b²=1 touch the circle x²+y²=r²

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