Chord of Contact of ellipse

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.

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.

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.

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.

From the point P ,the chord of contact to the ellipse E_(1):(x^(2))/(a)+(y^(2))/(b)=(a+b) touches the ellipse E_(2):(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 Then the locus of point P

Statement 1 : Tangents are drawn to the ellipse (x^2)/4+(y^2)/2=1 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

Statement 1 : Tangents are drawn to the ellipse (x^2)/4+(y^2)/2=1 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 (x x_1)/(a^2)+(y y_1)/(b^2)-1=0

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

Find the equation of the chord of contact of the point (3,1) to the ellipse x^2+9y^2=9 . Also find the mid-point of this chord of contact.

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.