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.

The auxiliary circle of the ellipse x^(2)/25 + y^(2)/16 = 1

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

The tangent at a point P(acosvarphi,bsinvarphi) of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 meets its auxiliary circle at two points, the chord joining which subtends a right angle at the center. Find the eccentricity of the ellipse.

The tangent at a point P(acosvarphi,bsinvarphi) of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 meets its auxiliary circle at two points, the chord joining which subtends a right angle at the center. Find the eccentricity of the ellipse.

If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts equal lengths l on the axes, then find ldot

Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the 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 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

If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)

A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 in which O A=a ,O B=b . Then find the area between the arc A B and the chord A B of the ellipse.