If e 1 and e 2 are respectively the eccentricities of the ellipse and the hyperbola , then write the value of 2e 1 2 + e 2 2 .

Question

Philoid · Accepted Answer

Given: e₁ and e₂ are respectively the eccentricities of the ellipse and the hyperbola

To find: value of 2e₁² + e₂²

Eccentricity(e) of hyperbola is given by,

Here a = 3 and b = 2

Therefore,

For ellipse:

Eccentricity(e) of ellipse is given by,

Therefore,

Substituting values from (1) and (2) in 2e₁² + e₂²

2e₁² + e₂²

= 3

Hence, value of 2e₁² + e₂² is 3

If e1 and e2 are respectively the eccentricities of the ellipse and the hyperbola , then write the value of 2e12 + e22.