Create an educational image representing conic sections. Illustrate circle, ellipse, and hyperbola on separate set of axes, each centered at (0,0). Depict the circle with a radius of 3 units, an ellipse with major axis length of 5 units and minor axis length of 3 units, and a hyperbola with a transverse axis of 5 units. For visual clarity, show lines of symmetry, intercepts, domain, and range for each conic section.

Can someone check my answers on exploring conic sections?

1. Graph x2 + y2 = 9. What are its lines of symmetry?

Every line through the center is a line of symmetry.

The y-axis and the x-axis are lines of symmetry.( my choice)

Every line through the center is a line of symmetry.

The y-axis and the x-axis are lines of symmetry.

2. Graph x2 + 9y2 = 25. What are the domain and range?

Domain: ¨C3 ¡Ü x ¡Ü 3
Range: ¨C3 ¡Ü y ¡Ü 3

Domain: ¨C5 ¡Ü x ¡Ü 5
Range: ¨C5 ¡Ü y ¡Ü 5 (my choice)

Domain: ¨C5 ¡Ü x ¡Ü 5
Range: ¨C1.67 ¡Ü y ¡Ü 1.67

Domain: ¨C1.67 ¡Ü x ¡Ü 1.67
Range: ¨C5 ¡Ü y ¡Ü 5

3. Graph x2 ¨C y2 = 16. What are its lines of symmetry?

It has four lines of symmetry, the x-axis, the y-axis, y = x, and y = ¨Cx.

Every line through the center is a line of symmetry.

It has four lines of symmetry, the x-axis, the y-axis, y = x, and y = ¨Cx.

It has two lines of symmetry, the x-axis and the y-axis. ( my choice)

4. Identify the center and intercepts of the conic section. Then find the domain and range.

The center of the ellipse is (0, 0).
The x-intercepts are (0, 5) and (0, ¨C5).
The y-intercepts are (¨C3, 0) and (3, 0).
The domain is {x | ¨C3 ¡Ü x ¡Ü 3}.
The range is {y { ¨C5 ¡Ü y ¡Ü 5}.

The center of the ellipse is (0, 0).
The x-intercepts are (¨C3, 0) and (3, 0).
The y-intercepts are (0, 5) and (0, ¨C5).
The domain is {x | ¨C3 ¡Ü x ¡Ü 3}.
The range is {y { ¨C5 ¡Ü y ¡Ü 5}.( my choice)

The center of the ellipse is (0, 0).
The x-intercepts are (0, 5) and (0, ¨C5).
The y-intercepts are (¨C3, 0) and (3, 0).
The domain is {y { ¨C5 ¡Ü y ¡Ü 5}.
The range is {x | ¨C3 ¡Ü x ¡Ü 3}.

The center of the ellipse is (0, 0).
The x-intercepts are (0, 5) and (0, ¨C5).
The y-intercepts are (¨C3, 0) and (3, 0).
The domain is {y { ¨C5 ¡Ü y ¡Ü 5}.
The range is {x | ¨C3 ¡Ü x ¡Ü 3}.

5. Identify the center and intercepts of the conic section. Then find the domain and range.

The center of the hyberbola is (0, 0).
The y-intercepts are (0, 5) and (0, ¨C5).
The domain is all real numbers.
The range is {y | y ¡Ý ¨C5 or y ¡Ü 5}.

The center of the hyberbola is (0, 0).
The x-intercepts are (0, 5) and (0, ¨C5).
The domain is all real numbers.
The range is {y | y ¡Ü ¨C5 or y ¡Ý 5}.

The center of the hyberbola is (0, 0).
The y-intercepts are (0, 5) and (0, ¨C5).
The domain is all real numbers.
The range is {y | y ¡Ü ¨C5 or y ¡Ý 5}.(my choice)

The center of the hyberbola is (0, 0).
The x-intercepts are (0, 5) and (0, ¨C5).
The domain is all real numbers.
The range is {x | x ¡Ü ¨C5 or x ¡Ý 5}.

a.

c.
d.
b.
c.

To make this thread clear,

a.
c.
d.
b.
c.

ARE the correct answers! I recently took this the other day and got a 5/5. Ignore the other comments trying to mislead everyone..

Thanks^^ 100% right

1. Graph x^2 + y^2 = 9. What are its lines of symmetry? Ans: A (Every line through the center is a line of symmetry).

2.Graph x^2 + 9y^2 = 25. What are the domain and range?
Ans: C
Domain: –5 ≤ x ≤ 5
Range: –1.67 ≤ y ≤ 1.67
3. Graph x2 – y2 = 16. What are its lines of symmetry?
Ans: D (It has two lines of symmetry, the x-axis and the y-axis).
4. Identify the center and intercepts of the conic section. Then find the domain and range.
Ans: B. The center of the ellipse is (0, 0).
The x-intercepts are (–3, 0) and (3, 0).
The y-intercepts are (0, 5) and (0, –5).
The domain is {x | –3 ≤ x ≤ 3}.
The range is {y { –5 ≤ y ≤ 5}.
5. Identify the center and intercepts of the conic section. Then find the domain and range.
Ans: C. The center of the hyperbola is (0, 0).
The y-intercepts are (0, 5) and (0, –5).
The domain is all real numbers.
The range is {y | y ≤ –5 or y ≥ 5}.

Thomas Is correct

A

C
D
B
C
Correct as of 6 March 2021
Exploring Conic Sections Quick Check

The correct answers are

A
C
D
B
C
I just took the test. 5/21/2020

A

C
D
B
C
Took the quick check 100% correct 12/7/2020

A

C
D
B
C
Exploring Conic Sections - Quick Check 100%
5/5/2020

Chai's answer's are all right, just got a 100%, thanks buddyo