If ` e_(1) , e_(2) " and " e_(3)` the eccentricities of a parabola , and ellipse and a hyperbola respectively , then

If eccentricities of a parabola and an ellipse are e and e' respectively, then

If eccentricities of a parabola and an ellipse are e and e' respectively, then

If e_1 and e_2 are the eccentricities of a parabola and ellipse respectively, then:

If e_(1) and e_(2) are the eccentricities of the hyperbola and its conjugate hyperbola respectively then (1)/(e_(1)^(2))+(1)/(e_(2)^(2)) is equal to

If e_(1) and e_(2) are the eccentricities of a hyperbola and its conjugate then

An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse.If e_(1) and e_(2) are the eccentricities of the ellipse and the hyperbola,respectively, then prove that (1)/(e_(1)^(2))+(1)/(e_(2)^(2))=2

If e and e' are the eccentricities of a hyperbola and its conjugate hyperbola respectively then prove that 1/e^2+1/(e')^2=1

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

If radii of director circles of (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are 2r and r respectively,let e_(E) and e_(H) are the eccentricities of ellipse and hyperbola respectively,then