Question

: What are the coordinates of the center of the ellipse shown below?

(x-1)^2 (y+5)^2
--------- + ----------- = 1
9 16

A: (5, -1)
B: (1, -5)
C: (3,4)
D: (-3, -4)



: What is the length of the major axis of the ellipse shown below?

(x-1)^2 (y+5)^2
--------- + ---------- = 1
9 16

A: 4
B: 8
C: 32
D: 16

Answer 1

Answer on Question #57272 – Math – Analytic Geometry

Question

1. What are the coordinates of the center of the ellipse shown below?

$$\frac{(x - 1)^2}{9} + \frac{(y + 5)^2}{16} = 1$$

A: (5; -1)

B: (1; -5)

C: (3; 4)

D: (-3; -4)

Solution

The equation of an ellipse is

$$\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 1,$$

where $(x_0; y_0)$ is the coordinates of the center, $a$ is the semi-major axis and $b$ is the semi-minor axis ($a > b$).

So, (1; -5) is the center of the ellipse.

**Answer:** B. (1; -5).

Question

2. What is the length of the major axis of the ellipse shown below?

$$\frac{(x - 1)^2}{9} + \frac{(y + 5)^2}{16} = 1$$

A: 4

B: 8

C: 32

D: 16

Solution

The equation of an ellipse is

$$\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 1,$$

where $(x_0; y_0)$ is the center.

So, in this case $a = 3$ and $b = 4$. Therefore, the length of the semi-major axis is 4 (because $4 > 3$) and the length of the major axis is $2b = 2 \cdot 4 = 8$.

**Answer:** B. 8.

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