" The Foci of the ellipse "(x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a

A parabola is drawn whose focus is one of the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (where a>b) and whose directrix passes through the other focus and perpendicular to the major axes of the ellipse.Then the eccentricity of the ellipse for which the length of latus-rectum of the ellipse and the parabola are same is

Let S and S' be the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is e. P is a variable point on the ellipse. Consider the locus the incentre of DeltaPSS' . The locus of the incenter is a\an

If the lines joining the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , where agtb and an extremity of its monor axis are inclined at an angle 60^(@) , then the eccentricity of the ellipse 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

A parabola is drawn with focus at one of the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1. If the latus rectum of the ellipse and that of the parabola are same,then the eccentricity of the ellipse is 1-(1)/(sqrt(2)) (b) 2sqrt(2)-2sqrt(2)-1( d) none of these

Let S and S'' be the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is i.e. P is a variable point on the ellipse. Consider the locus of the incenter of DeltaPSS'' The maximum area of recatangle inscribed in the locus is

Let S and S'' be the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is i.e. P is a variable point on the ellipse. Consider the locus of the incenter of DeltaPSS'' The maximum area of recatangle inscribed in the locus is

Let S and S'' be the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is i.e. P is a variable point on the ellipse. Consider the locus of the incenter of DeltaPSS'' The maximum area of recatangle inscribed in the locus is

F is one of the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with O as centre. bar(AB) and bar(CD) are major and minor axes respectively. If OF=6 and the diameter of the incircle of triangle OCF is 2. The values of a & b are