If `e_1` and `e_2` are the eccentricities of the hyperbola `x^2/a^2-y^2/b^2=1` and `y^2/b^2-x^2/a^2=1` then show that `1/e_1^2+1/e_2^2=1`.

The eccentricity of the hyperbola y^2/25-x^2/144=1 , is:

For the standard hyperbola x^2/a^2-y^2/b^2=1 ,

If e_1 and e_2 be the eccentricities of two conjugate hyperbola, then 1/e_1^2+1/e_2^2 is :

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 a hyperbola and its conjugate, prove that: 1/e_1^2+1/e_2^2=1

The eccentricity of the hyperbola (sqrt(1999))/(3)(x^(2)-y^(2))=1 , is

If the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1and(y^(2))/(b^(2))-(x^(2))/(a^(2))=1" are "e_(1)ande_(2) respectively then prove that : (1)/(e_(1)^(2))+(1)/(e_(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

The eccentricities of two ellipses x^2/144+y^2/25=1 and x^2/a^2+y^2/b^2=1 are equal, then the value of a/b is :

The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is