The major and minor axes of an ellipse are along the X -axis and Y -axis respectively. If its latusrectum is of length 4 and the distance between the foci is 4 2 , then the equation of that ellipse is

Step-by-step solution

Let the equation of ellipse Length of latusrectum of ellipse (i) is and distance between the foci is array rlr & 2 a e=4 2 & & a 1- b^2 a^2 =2 2 & [ e= 1- b^2 a^2 ,(b>a) ] & a^2-b^2=8 & & a^2-2 a-8=0 & [from Eq. (ii) ., b^2=2 a ] & (a-4)(a+2)=0 & & a=4,-2 & & a=4 & a>0 array So, b^2=8 Equation of required ellipse is aligned & x^2 16 + y^2 8 =1 x^2+2 y^2 & =16 aligned Hence, option (b) is correct.