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?

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Answer 1 · 2016-10-04T19:26:51

#"a Circle : Centre "(-2,3)", &, radius "r=3.#

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

#:. x^2+4x+4+y^2-6y+9=9#

#:. (x+2)^2+(y-3)^2=3^2#

We know that, the eqn. #(x-h)^2+(y-k)^2=r^2,# represents a

Circle having Centre at the pt.#(h,k)# and radius #r.#

Hence, the given eqn. represents,

#"a Circle : Centre "(-2,3)", &, radius "r=3.#