1. ## Conic Sections

Problem:$\displaystyle 4x^2 + 4x +y^2 = 0$

I graph it and I get an elipse, but I cant figure out how to get it into the form:
$\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} =1$

I've using the form:

$\displaystyle b^2x^x + a^2y^2 = a^2b^2$

and setting:

$\displaystyle a^2b^2 = -4x$

But, nothing came good out of that.

Any suggestions?

2. Originally Posted by Sw0rDz
Problem:$\displaystyle 4x^2 + 4x +y^2 = 0$

I graph it and I get an elipse, but I cant figure out how to get it into the form:
$\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} =1$

I've using the form:

$\displaystyle b^2x^x + a^2y^2 = a^2b^2$

and setting:

$\displaystyle a^2b^2 = -4x$

But, nothing came good out of that.

Any suggestions?
$\displaystyle 4x^2 + 4x +y^2 = 0$

$\displaystyle 4\left(x^2 + x + \frac{1}{4}\right) + y^2 = 1$

$\displaystyle 4\left(x + \frac{1}{2}\right)^2 + y^2 = 1$

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

3. Originally Posted by skeeter
$\displaystyle 4x^2 + 4x +y^2 = 0$

$\displaystyle 4\left(x^2 + x + \frac{1}{4}\right) + y^2 = 1$

$\displaystyle 4\left(x + \frac{1}{2}\right)^2 + y^2 = 1$

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

Awh!! Thankyou!