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?

Question

1699 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-18T16:20:29

See explanation.

The equation

#ax^2+2hxy+by^2+2gx+2fy+c=0#

(i) represents a circle, if #a = b and h = 0#.

(ii) a parabola, if #ab=h^2#,

(iii) an ellipse, if #a b-h^2 > 0#,

(iv) a hyperbola, if #ab - h ^2 < 0 # and

(v) a pair of straight lines, if #abc+2fgh-ag^2-bf^2-ch^2=0#.

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

In the standard form, it is

#(x-1/2)^2+y^2=(3/2)^2#

The center is (1/2, 0) and the radius is #3/2#.

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