Question

If `a(x^(2)+y^(2)+2y+1)=(x-2y+3)^(2)` is an ellipse and `a in (b, oo)`, then the value of b is ___________

Answer 1

`a(x^(2)+y^(2)+2y+1)=(x-2y+3)^(2)`
`rArra(x^(2)+(y+1)^(2))=(x-2y+3)^(2)`
`rArr sqrt(x^(2)+(y+1)^(2))=(sqrt(5))/(sqrt(a))(|x-2y+3|)/(sqrt(5))`
This represents ellipse if `e=(sqrt(5))/(sqrt(a))lt1`
This given `a in (5,oo)`