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The equation of the ellipse having a ver...

The equation of the ellipse having a vertex at (6,1) a focus at (4,1) and the eccentricity `(3)/(5)` is
1) `((x-1)^(2))/(16)+((y-1)^(2))/(25)=1` (2) `((x-1)^(2))/(25)+((y-1)^(2))/(16)=1`
3) `((x+1)^(2))/(25)+((y+1)^(2))/(16)=1` (4) `((x+1)^(2))/(16)+((y+1)^(2))/(25)=1`

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An ellipse has its centre at (1,-1) and semi major axis =8 and it passes through the point (1,3). The equation of the ellipse is ((x+1)^(2))/(64)+((y+1)^(2))/(16)=1b((x-1)^(2))/(64)+((y-1)^(2))/(16)=1c((x-1)^(2))/(64)+((y-1)^(2))/(16)=1d((x-1)^(2))/(64)+((y-1)^(2))/(16)=1

For the given ellipse ,find the equation of directrix (i) (x^(2))/(25) + (y^(2))/(9) = 1 iii (x^(2))/(36) + (y^(2))/(16) = 1 (x^(2))/(49) + (y^(2))/(36) = 1 (iv) (x^(2))/(100) + (y^(2))/(400) = 1.

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Statement 1: Two ellipses (x^(2))/(16)+(y^(2))/(9)=1 and (x^(2))/(9)+(y^(2))/(16)=1 are congruent.Statement 2:(x^(2))/(16)+(y^(2))/(16)=1 and (x^(2))/(9)+(y^(2))/(16)=1 have same eccentricity