`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:

The eccentricity of the ellipse 5x^(2) + 9y^(2) = 1 is _

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

S_(1) ,S_(2) are two foci of the ellipse x^(2) + 2y^(2) = 2 . P be any point on the ellipse The locus incentre of the triangle PSS_(1) is a conic where length of its latus rectum is _

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

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

S , T are two foci of an ellipse and B is a one end point of minor axis . If STB be a equilateral triangle and eccentricity of the ellipse be (1)/(lambda) , then the value of lambda is _

(5,-4) and (-3, 2) are two foci of an ellipse whose eccentricity is 2/3. Then the length of the minor axis of the ellipse is-

Consider an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a gt b) . A hyperbola has its vertices at the extremities of minor axis of the ellipse and the length of major axis of the ellipse is equal to the distance between the foci of hyperbola. Let e_(1) and e_(2) be the eccentricities of ellipse and hyperbola, respectively. Also, let A_(1) be the area of the quadrilateral fored by joining all the foci and A_(2) be the area of the quadrilateral formed by all the directries. The relation between e_(1) and e_(2) is given by

Pa n dQ 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 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x^(2)+4y^(2)=36