If the distance of the centre of the ellipse `4(x-2y+1)^2+9(2x+y+2)^2=25` from the origin is `lambda` times its eccentricity,then find the value of `5lambda^2`

Explanation

Given equation of ellipse,

`4(x-2y+1)^2+9(2x+y+2)^2 = 25`

`=>(x-2y+1)^2/(5/2)^2+(2x+y+2)^2/(5/3)^2 = 1`

This is standard equation for an ellipse with `a = 5/2 and b = 5/3`

Now, center of ellipse will be the interesction of below two equations,

`x-2y+1 = 0->(1)`

`2x+y+2 = 0->(2)`

Multiplying (2) with `2` and then adding in (1),

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