The sum of the squares of the eccentricities of the conics x² 4 + y² 3 =1 and x² 4 - y² 3 =1 is

Step-by-step solution

Given, equation of ellipse is, x² 4 + y² 3 =1 and equation of hyperbola is x² 4 - y² 3 =1 Eccentricity of ellipse is e₁= a²-b² a² = 4-3 4 = 1 2 and eccentricity of hyperbola is e₂= a²+b² a² = 4+3 4 = 7 2 Sum of the squares of the eccentricities aligned &=e₁²+e₂²= ( 1 2 )²+ ( 7 2 )² &= 1 4 + 7 4 = 8 4 =2 aligned