1. ## Ellipse

The ellipse $\displaystyle 14x^2+2x+y^2 = 1$ has its center at the point (b, c) where
$\displaystyle b =$
$\displaystyle c =$
The length of the major diameter of this ellipse is __

2. can someone move this thread over to Calculus section, i posted this in the wrong section.

3. $\displaystyle 14x^{2}+2x+y^{2}=1$

Complete the square and get:

$\displaystyle 14(x+\frac{1}{14})^{2}+y^{2}=\frac{15}{14}$

$\displaystyle \frac{196(x+\frac{1}{14})^{2}}{15}+\frac{14y^{2}}{ 15}=1$

To find the x intercepts, set y=0 and solve for x, getting $\displaystyle x=(\frac{-(\sqrt{15}+1)}{14},\frac{\sqrt{15}-1}{14})$

The center is at (-1/14,0)

$\displaystyle b=\frac{-1}{14}+\frac{\sqrt{15}-1}{14}=\frac{\sqrt{15}}{14}$

Setting y=-1/14 in the equation gives us major axes of $\displaystyle a=(\frac{\sqrt{210}}{14}, \frac{-\sqrt{210}}{14})$

The foci, c, can be found by $\displaystyle c^{2}=a^{2}-b^{2}$

$\displaystyle c=\sqrt{(\frac{\sqrt{210}}{14})^{2}-(\frac{\sqrt{15}}{14})^{2}}=\pm\frac{\sqrt{195}}{1 4}$