Prove that the chord of contact of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` with respect to any point on the directrix is a focal chord.

The locus of mid-points of a focal chord of the ellipse x^2/a^2+y^2/b^2=1

Prove that the chords of contact of pairs of perpendicular tangents to the ellipse x^2/a^2+y^2/b^2=1 touch another fixed ellipse.

Prove that the chords of contact of pairs of perpendicular tangents to the ellipse x^2/a^2+y^2/b^2=1 touch another fixed ellipse.

The locus of the poles of normal chords of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

The locus of the poles of normal chords of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

Find the locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 form a triangle of constant area with the coordinate axes.

Statement 1 : Tangents are drawn to the ellipse (x^2)/4+(y^2)/2= at the points where it is intersected by the line 2x+3y=1 . The point of intersection of these tangents is (8, 6). Statement 2 : The equation of the chord of contact to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 from an external point is given by (xx_1)/(a^2)+(y y_1)/(b^2)-1=0

The chord of contact of (2,1) with respect to the circle x^(2)+y^(2)=2 is

If alpha-beta is constant prove that the chord joining the points alpha and beta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 touches a fixed ellipse

The locus of mid point of focal chords of ellipse x^2 / a^2 +y^2/b^2 =1