An ellipse passing through (4 2 , 2 6 ) has foci at (-4,0) and (4,0) . Then, its eccentricity is

Step-by-step solution

The y -coordinate of foci is zero Major axis is on X -axis ae =4 Let, equation of ellipse be aligned & x^2 a^2 + y^2 b^2 =1 & (4 2 )^2 a^2 + (2 6 )^2 a^2-16 & [ b^2=a^2 (1-e^2 )=a^2-16 . & 32 a^2 + 24 a^2-16 =1 & 32 a^2-512+24 a^2=a^2 (a^2-16 ) & 56 a^2-512=a^4-16 a^2 & a^4-72 a^2+512=0 & a^2-64 a^2-8 a^2+512=0 & a^2 (a^2-64 )-8 (a^2-64 )=0 & (a^2-8 ) (a^2-64 )=0 & a^2=64 a=8 & ( a^2=8 . is not possible) & ae =4 8 e=4 & aligned e= 1 2