# Thread: Analytic Geometry- Analyse y^2 + 6y +2x + 1 = 0

1. ## Analytic Geometry- Analyse y^2 + 6y +2x + 1 = 0

Hello,

I need help with this problem:

Analyze the equation y^2 + 6y +2x + 1 = 0

By analyze the problem means to find the center, foci, and vertices.

I do not know how to get this equation into standard form. (I believe that is the goal.)

2. ## Re: Analytic Geometry- Analyze the equation

Originally Posted by dazedandmathfused
Hello,

I need help with this problem:

Analyze the equation y^2 + 6y +2x + 1 = 0

By analyze the problem means to find the center, foci, and vertices.

I do not know how to get this equation into standard form. (I believe that is the goal.)

\displaystyle \begin{align*} y^2 + 6y + 2x + 1 &= 0 \\ y^2 + 6y &= -2x - 1 \\ y^2 + 6y + 3^2 &= -2x - 1 + 3^2 \\ \left(y + 3\right)^2 &= -2x+ 8 \\ \left(y + 3\right)^2 - 8 &= -2x \\ x &= -\frac{1}{2}\left(y + 3\right)^2 + 4 \end{align*}

This is a quadratic. What information can you gain now?

3. ## Re: Analytic Geometry- Analyze the equation

Originally Posted by Prove It
\displaystyle \begin{align*} y^2 + 6y + 2x + 1 &= 0 \\ y^2 + 6y &= -2x - 1 \\ y^2 + 6y + 3^2 &= -2x - 1 + 3^2 \\ \left(y + 3\right)^2 &= -2x+ 8 \\ \left(y + 3\right)^2 - 8 &= -2x \\ x &= -\frac{1}{2}\left(y + 3\right)^2 + 4 \end{align*}

This is a quadratic. What information can you gain now?
Well for this equation I would complete the square. I belive standard form of an elipse will be the result. I do not know how to do this.

Is that basically what you did?

4. ## Re: Analytic Geometry- Analyze the equation

Originally Posted by dazedandmathfused
Well for this equation I would complete the square. I belive standard form of an elipse will be the result. I do not know how to do this.

Is that basically what you did?
I have ALREADY completed the square to give you a QUADRATIC in standard form. A Quadratic is NOT an Ellipse.

5. ## Re: Analytic Geometry- Analyze the equation

Originally Posted by dazedandmathfused
Well for this equation I would complete the square. I belive standard form of an elipse will be the result. I do not know how to do this.

Is that basically what you did?
If you cannot recognise that post # 2 explicitly shows a (sideways) parabola then you need to go back and thoroughly revise your class notes and textbook.