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.

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

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.

The maximum distance of the centre of the ellipse (x^(2))/(16) +(y^(2))/(9) =1 from the chord of contact of mutually perpendicular tangents of the ellipse is

Chord | Chord of Contact | Chord With Given Mid Point and Problem Solving

For the ellipse (x^(2))/(16)+(y^(2))/(9)=1 .If The maximum distance from the centre of the ellipse to the chord of contact of mutually perpendicular tangents is lambda then 5 lambda-10=

Chord of Contact | Chord With Given Mid Point and Problem Solving

Chord of contact of tangents drawn from the point M(h, k) to the ellipse x^(2) + 4y^(2) = 4 intersects at P and Q, subtends a right angle of the centre theta