Find the center, vertices, and foci of the ellipse given by the equation.
A)center: , vertices: , foci:
B)center: , vertices: , foci:
C)center: , vertices: , foci:
D)center: , vertices: , foci:
E)center: , vertices: , foci:

Question

Find the center, vertices, and foci of the ellipse given by the equation. 
A)center: , vertices: , foci: 
B)center: , vertices: , foci: 
C)center: , vertices: , foci: 
D)center: , vertices: , foci: 
E)center: , vertices: , foci:

Quizplus · Accepted Answer

Comparing the given equation with the standard form of the equation of an ellipse,

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1$

we can see that the center is at $(h,k) = (3,-4)$, and $a = 5$ and $b = 3$.

The distance between the center and each vertex is $a = 5$, and the vertices are located at $(3 \pm 5, -4) = (8, -4)$ and $(-2, -4)$.

The distance between the center and each focus is given by $c = \sqrt{a^2-b^2} = 4$, and the foci are located at $(3 \pm 4, -4) = (7, -4)$ and $(-1, -4)$. Thus, the answer is (C).

Find the Center, Vertices, and Foci of the Ellipse Given