Question

how do i factor this equation? and how am i supposed to graph it? x^2 + y^2 + 6x - 8 = 0

Answer 1

Solve for y

Answer 2

x^2 + 6x + y^2 = 8
x^2 + 6x + 9 + y^2 = 8 + 9
(x+3)^2 + y^2 = 17
This is a circle equation with center at (-3,0) and radius is squroot( 17). So locate the center...and draw a circle with that radius around it

Answer 3

(x² + 6x + 9) + y² = 8 + 9
(x + 3)² + y² = 17
Circle, centered at (-3,0) with a radius of √17

Answer 4

i'm confused. how did you get the plus nine?

Answer 5

Completes the Square

Answer 6

general eq of the circle is
x^2+y^2+2gx+2fy+c=0

Answer 7

Completing the square. In order to eliminate the x-term, you create a square with the constant term. In order to determine how much constant you need, you just half the coefficient of the x term (6 → 3), then square that → 9. Then add that to both sides

Answer 8

centre (-g,-f) and radius sqrt(g^2+f^2-c)

Answer 9

Here's a graph of the circle.
http://www.wolframalpha.com/input/?i=plot+%28x+%2B+3%29%C2%B2+%2B+y%C2%B2+%3D+17

Answer 10

thank you, all of you
i don't even know how to identify what type of equation this is.

Answer 11

The x^2 +y^2 on one side usually means a circle

Answer 12

if you have +x^2 and +y^2 on the same side, it's either a circle or ellipse
if it's +x^2 - y^2 or -x^2 + y^2, that's a (rectangular) hyperbola

Answer 13

I think I deserve the credit for this one. I answered it in the least amount of statements.

Answer 14

Well thank you pkrkc

Answer 15

thank you for helping me

Answer 16

I would've provided more complete answers but those other guys type way faster than I do

Answer 17

it's confusing having so many people help me at once. but you at least all had it right

Answer 18

so once i plot (-3,0), i go up three? and over three?