An ellipse having the coordinate axes as its axes and its major axis along Y -axis, passes through the point (-3,1) and has eccentricity 2 5 . Then its equation is

Step-by-step solution

Let the equation of ellipse is aligned & x^2 a^2 + y^2 b^2 =1 & e= 2 5 & a^2-b^2 a^2 = 2 5 & a^2-b^2 a^2 = 2 5 & 5 a^2-5 b^2=2 a^2 & aligned Given, array ll & 3 a^2=5 b^2 & a^2= 5 b^2 3 array Now, ellipse passes through (-3,1) aligned & (-3)^2 a^2 + (1)^2 b^2 =1 9 b^2+a^2=a^2 b^2 & 9 b^2+ 5 b^2 3 = 5 b^4 3 32 b^2 3 = 5 b^4 3 & b^2= 32 5 aligned From Eq. (i), we get array rlrl & & x^2 32 + y^2 32 3 & =1 & 3 x^2+5 y^2 & =32 & & 3 x^2+5 y^2-32 & =0 . array