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`

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

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

If e and e' are the eccentricities of a hyperbola and its conjugate, then the locus of the points (e,e') is

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

If e and e' be the eccentricities of two conics S=0 and S'=0 and if e^(2)+e'^(2)=3 , then both S and S' can be

Find the equation of the hyperbola, given that : centre (1,-2), e=3/2 , LR=5

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_1 and E_2 are equally likely, mutually exclusive and exhaustive events and P(A/E_1)=0.2, P(A/E_2)=0.3 , find P(E_1/A)