Foci of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1(alt b)` are

The locus of the point of inter section of perpendicular chords passing through the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) is

Equations of the directrices of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) are

If e' is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 (a gt b) , then

if S and S are two foci of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 ( altb ) and P(x_(1) , y_(1)) a point on it then SP+ S'P is equal to

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

S and T are the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and B is an end of the minor axis.If STB is an equilateral triangle,the eccentricity of the ellipse is e then find value of 4e

If S and S' are two foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and B is and end of the minor axis such that Delta BSS' is equilateral,then write the eccentricity of the ellipse.

If the circle whose diameter is the major axis of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a gt b gt 0) meets the minor axis at point P and the orthocentre of DeltaPF_(1)F_(2) lies on the ellipse, where F_(1) and F_(2) are foci of the ellipse, then the square of the eccentricity of the ellipse is

If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

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