`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:

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

if vertices of an ellipse are (-4,1),(6,1) and x-2y=2 is focal chord 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 . . .

Let S and S' be the fociof 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 incenter of DeltaPSS' The eccentricity of the locus of the P is

P and Q 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 P B Q is an equilateral triangle, then the eccentricity of the ellipse is

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

Consider the ellipse whose major and minor axes are x-axis and y-axis, respectively. If phi is the angle between the CP and the normal at point P on the ellipse, and the greatest value tan phi is 3/4 (where C is the centre of the ellipse). Also semi-major axis is 10 units . The eccentricity of the ellipse is

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

If the foci of an ellipse are (0,+-1) and the minor axis is of unit length, then find the equation of the ellipse. The axes of ellipse are the coordinate axes.