# Thread: Find the center, vertices, foci and eccentricity

1. ## Find the center, vertices, foci and eccentricity

Find the center, vertices, foci and eccentricity of the ellipse given by the following problem.
x^2 / 11 + y^2 / 36 =1. Did I do it right? Thanks
Center: (0,0)
Vertices: (0,6) and (0,-6)
Foci: (0,5) and (0, -5)
eccentricity= 5/6
a^2=36 a=6
b^2=11 b=square root of 11 = 3.32
a^2=b^2+c^2
36=11+c^2
25=C^2
c=5
e=c/a = 5/6

2. ## values of ellipse

$
\frac{\left(x - h\right)^2}{b^2} + \frac{\left(y - k\right)^2}{a^2} = 1
\Rightarrow
\frac{x^2}{11} + \frac{y^2}{36} = 1
$

major axis is parallel to the y axis
Center is $(h,k)\ h=0,\ k=0,\ \Rightarrow(0,0)$
Vertices are $(h,k+a)\ (h,k-a)\ 0+6,\ 0-6 \Rightarrow \pm6$
Foci $(h,k+c)\ (h,k-c) \ 0,0+5\ 0,0-5 \Rightarrow (0,5)\ (0,-5)$
eccentricty $\frac{e}{c}\ \Rightarrow \frac{5}{6}$