1. ## Ecentricity

How do you find the eccentricity of 4x^2 + 16y^2 + 8x +64y +4 = 0

2. Originally Posted by jumpman23
How do you find the eccentricity of 4x^2 + 16y^2 + 8x +64y +4 = 0
1. By completing the square you get:

$4x^2 + 16y^2 + 8x +64y +4 = 0$

$4(x^2+2x\bold{\color{blue}+1}) + 16(y^2 +4y \bold{\color{red}+4}) = -4\bold{\color{blue}+4}\bold{\color{red}+64}$

$\dfrac{(x+1)^2}{16}+\dfrac{(y+2)^2}{4}=1$

2. You are supposed to know that

$e^2+b^2=a^2$ Plug in the values you know and calculate e:

$e^2=16-4=12~\implies~\boxed{e=2\sqrt{3}}$

3. thanks

4. Sorry, earboth the answer is wrong.The curve in question is an ellilse whose eccentricity must be less than $1$.

The formula used by you for calculating eccentricity is wrong.It should be

$
a^2=b^2+a^2e^2
$

Thus $e=\frac{\sqrt{3}}{2}$

5. Originally Posted by pankaj
Sorry, earboth the answer is wrong.The curve in question is an ellilse whose eccentricity must be less than $1$.

The formula used by you for calculating eccentricity is wrong.It should be

$
a^2=b^2+a^2e^2
$

Thus $e=\frac{\sqrt{3}}{2}$

1. there exist a linear eccentricity $e^2=a^2-b^2$. That's the eccentricity I've calculated.

2. there exist a numerical eccntricity $\dfrac ea=\epsilon$. Obviously this is the eccentricity you've had in mind.

(Remark: I translated the technical terms literally from German so maybe the English expressions differ a bit)

6. To confirm the formula they gave you in your book for the eccentricity of an ellipse, and for worked examples of how to find the eccentricity, try some online lessons.

Then make sure that you memorize the formula before your next test!!

1. there exist a linear eccentricity $e^2=a^2-b^2$. That's the eccentricity I've calculated.
2. there exist a numerical eccntricity $\dfrac ea=\epsilon$. Obviously this is the eccentricity you've had in mind.