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

The locus of middle point of the chord of the ellipse x²/a²+y²/b²=1 touching the ellipse The locus of midpoint of the chord of the ellipse x²/α²+y²/β²=1

The points on the ellipse x²/25+y²/9=1 whose angles differ by a right angle are

The chord of contact of tangents drawn from points on x²/a²+y²/b²=1 to the circle x²+ y²=c² touches the ellipse

The tangents are drawn to the ellipse x²/a²+y²/b²=1 at point where it is intersected by the line lx+my+n=0. The point of intersection of tangents at these points is

If the lines 4x+3y-1=0,x-y+5=0 and kx+5y-3=0 are concurrent,then k is equal to