`S_1, S_2`, are foci of an ellipse of major axis of length `10 units` and `P` is any point on the ellipse such that perimeter of triangle `PS_1 S_2`, is `15`. Then eccentricity of the ellipse is:

S and T are foci of an ellipse and B is an end of the minor axis , if STB is an equilateral triangle , the eccentricity of the ellipse , is

S and T are foci of an ellipse and B is an end of the minor axis , if STB is an equilateral triangle , the eccentricity of the ellipse , is

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

Let S=(3,4) and S'=(9,12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent of the ellipse is (1, -4) then the eccentricity of the ellipse 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 the m inor axis of an ellipse form s an equilateral triangle with one vertex of the ellipse then e =

Consider an ellipse x^2/a^2+y^2/b^2=1 Let a hyperbola is having its vertices at the extremities of minor axis of an ellipse and length of major axis of an ellipse is equal to the distance between the foci of hyperbola. Let e_1 and e_2 be the eccentricities of an ellipse and hyperbola respectively. Again let A be the area of the quadrilateral formed by joining all the foci and A, be the area of the quadrilateral formed by all the directrices. The relation between e_1 and e_2 is given by

If the area of a square circumscribing an ellipse is 10 square units and maximum distance of a normal from the centre of the ellipse is 1 unit, than find the eccentricity of ellipse

If the minor axis of an ellipse subtends an equilateral triangle with vertex at one end of major axis, then write the eccentricity of the ellipse.

Let S and S'' be the fociof 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 the incenter of DeltaPSS'' The eccentricity of the locus oc the P is (a) ellipse (b) hyperbola (a) parabola (d) circle