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

The equation of the chord of the ellipse 2x²+3y²=6 having (1, -1) as its midpoint is

The locus of the poles of chords of  the ellipse x²/a²+y²/b²=1 which touch The locus of the poles w.r.t the ellipse x²/α²+y²/β²=1 is

The tangent and normal to the ellipse 4x²+9y² =36 at a point P on it meets the major axis in Q nd R respectively. If QR=4, then the eccentric angle of P is

If the polar of (2, -1) with respect to the ellipse 3x²+4y²=12 is  ax+by+c=0 then the ascending order  of a, b, c is

The total number of real tangents that can be drawn to the ellipse 3x²+5y²=32 and 25x²+9y²=450 passing through (3, 5) is

If the equation of the pair of tangents drawn from (1, 2) on the ellipse x²+2y²=2 is 3x²-4xy-y²+ax+by+c=0 then the ascending order of a, b, c is

The pole of the line y=x+2 e with respect to the ellipse x²+4y²-2x-6y-10=0 is

The equation of ellipse whose focus is (0, √a²-b²), directrix is y=a²/√a²-b² and eccentricity is √a²-b²/a is