​ If the hyperbola x^2/a^2 - y^2/1 = 1 and the ellipse 3x^2 + 4y^2 = 12 have same latusrectum, ​

Question

If the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}1 = 1\) and the ellipse 3x² + 4y² = 12 have same latusrectum, then the value of \(12(e^2_H + e^2_E)\) is equal to (where e_H and e_E are eccentricities of hyperbola and ellipse respectively)

Answer 1

Given \(\frac{2(1)}{a} = \frac{2(3)}2\)