Answer to Question #270949 in Analytic Geometry for Angel Nodado

Question

Identify the center, vertices, and foci. Then sketch the graph.

((x + 3) ^ 2)/9 + (y ^ 2)/25 = 1

Answer 1

Since the denominator of $y^2$ is larger, the ellipse has a vertical major axis.

Standard form:

$$\dfrac{y^2}{25}+\dfrac{(x+3)^2}{9}=1$$

Center: $(-3, 0)$

$$a^2=25, b^2=9,$$

$$c^2=a^2-b^2=25-9=16, c=4$$

Foci: $(-3, -4), (-3, 4)$

Vertices: $(-3, -5), (-3, 5)$

Co-vertices: $(-6, 0), (0,0)$