From any point on any directrix of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1,a > b ,` a pari of tangents is drawn to the auxiliary circle. Show that the chord of contact will pass through the correspoinding focus of the ellipse.

From a point P tangents are drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 If the chord of contact touches the auxiliary circle then the locus of P is

Show that the feet of the perpendiculars from the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 on any of its tangents lie on its auxiliary circle

Tangents are drawn from each point on the line 2x+y=4 to the circle x^(2)+y^(2)=4 . Show that the chord of contact pass through a point (1/2,1/4) .

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 any point on the line y=x+4, tangents are drawn to the auxiliary circle of the ellipse x^2+4y^2=4 . If P and Q are the points of contact and Aa n dB are the corresponding points of Pa n dQ on he ellipse, respectively, then find the locus of the midpoint of A Bdot

Tangents are drawn to the ellipse x^(2)+2y^(2)=4 from any arbitrary point on the line x+y=4, the corresponding chord of contact will always pass through a fixed point, whose coordinates are

From any point on the line y=x+4 tangents are drawn to the auxiliary circle of the ellipse x^(2)+4y^(2)=4. If P and Q are the points of contact and A and B are the corresponding points of P and Q on he ellipse,respectively,then find the locus of the midpoint of AB.

Tangents are drawn from points on the line x-y+2=0 to the ellipse x^(2)+2y^(2)=4 then all the chords of contact pass through the point