# How do you identity if the equation x^2+y^2+4x-6y=-4 is a parabola, circle, ellipse, or hyperbola and how do you graph it?

Oct 4, 2016

$\text{a Circle : Centre "(-2,3)", &, radius } r = 3.$

#### Explanation:

Rewriting the given eqn., ${x}^{2} + {y}^{2} + 4 x - 6 y + 4 = 0$

Completing the square of ${y}^{2} - 6 y$

$\therefore {x}^{2} + 4 x + 4 + {y}^{2} - 6 y + 9 = 9$

$\therefore {\left(x + 2\right)}^{2} + {\left(y - 3\right)}^{2} = {3}^{2}$

We know that, the eqn. ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2} ,$ represents a

Circle having Centre at the pt.$\left(h , k\right)$ and radius $r .$

Hence, the given eqn. represents,

$\text{a Circle : Centre "(-2,3)", &, radius } r = 3.$