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

Dec 18, 2016

See explanation.

#### Explanation:

The equation

$a {x}^{2} + 2 h x y + b {y}^{2} + 2 g x + 2 f y + c = 0$

(i) represents a circle, if $a = b \mathmr{and} h = 0$.

(ii) a parabola, if $a b = {h}^{2}$,

(iii) an ellipse, if $a b - {h}^{2} > 0$,

(iv) a hyperbola, if $a b - {h}^{2} < 0$ and

(v) a pair of straight lines, if $a b c + 2 f g h - a {g}^{2} - b {f}^{2} - c {h}^{2} = 0$.

Here, a = b = 1 and h = 0.. It is a circle.

In the standard form, it is

${\left(x - \frac{1}{2}\right)}^{2} + {y}^{2} = {\left(\frac{3}{2}\right)}^{2}$

The center is (1/2, 0) and the radius is $\frac{3}{2}$.

graph{x^2+y^2-x-2=0 [-5, 5, -2.5, 2.5]} .