5 X^{2 }+ 2X + 5 Y^{2 } 3y 19 = 0
5 ( X^{2} + 2/5 X ) + 5 ( Y^{2}  3y ) = 19
5 ( X^{2 }+ 2/5 X + 1/25) + 5 ( Y^{2} 3/5y +9/100 ) = 19 +1/5 + 45/100
5 ( X + 1/5 ) ^{2 }+ 5 ( Y  3/10)^{2} = (1900 + 20 + 100)/100
( X + 1/ 5) ^{2 } + ( Y  3/10)^{2} = 2020/ 500 = 4.04 (**)
Centre: ( 1/5, 3/10) radius = 2
So, basically have to convert the expression to the form of ( **), by adding and subtracting quantities from both sides
first you factor out 5 from 5X^{2}, 5 Y^{2}
then make every parenthesis a perfect square, by adding quantities on both sides, and simplify it.
9/12/2013

Parviz F.