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  4. The equation x2 + y2 + 4x + 6y + 13 = 0 represents

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Q. The equation $ x^2 + y^2 + 4x + 6y + 13 = 0 $ represents

AMUAMU 2016

Solution:

We have,
$x^2 + y^2 + 4x + 6y + 13 = 0$
$ \Rightarrow (x^2 + 4x + 4) - 4 + ( y^2 + 6y +9 ) $
$ - 9 + 13 = 0$
$\Rightarrow ( x + 2)^2 + (y + 3)^2 - 13 + 13 = 0$
$\Rightarrow ( x + 2)^2 + ( y + 3)^2 = 0$
which is equation of a point circle.