How do you identity if the equation $x^2-8y+y^2+11=0$ is a parabola, circle, ellipse, or hyperbola and how do you graph it?

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Answer 1 · 2016-11-09T07:16:46

Circle

Modify the equation by completing the square for $y$ .

$x^2 + (y-4)^2 = 5$

The equation above describes a circle of radius $sqrt5$ centered at $(0,4)$ .

graph{x^2 + (y-4)^2 = 5 [-9.67, 10.33, -1.6, 8.4]}

Answer 2 · 2016-11-09T09:07:22

the eqn of a circle is $(x-a)^2+(y-b)^2+r^2$

when multiplied and simplified out the eqn can be rearranged to the form

$x^2+y^2+fx+gy+h=0$

note;

1) the coefficients of $x$ & $y$ are the same.

2) there are no $'xy'$ terms

Ellipses are of the form

$x^2/a+y^2/b=1$

hyperbolas are of the form

$x^2/a-y^2/b=1$

again no $'xy'$ terms.

How do you identity if the equation x^2-8y+y^2+11=0x^2-8y+y^2+11=0 is a parabola, circle, ellipse, or hyperbola and how do you graph it?