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

The product of the slopes of the tangents to the ellipse 2x²+3y²=6 draw from the point (1, 2) is

The ordinate PN of P(a cos θ, b sin θ) on the ellipse x²/a²+y²/b²=1 meets the auxiliary circle at Q,. The locus of the point of intersection of normal at P and Q is

The locus of the middle point of chords of the ellipse x²/a²+y²/b²=1   whose pole lies on the auxiliary circle is

The midpoint of a chord 4x+5y-13=0 of the ellipse 2x²+5y²=20 is