algebra

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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}.

  • algebra -

    #1. Every line through the center is an axis of symmetry. The x- and y- axes are just two of them.

    #2. Not sure what the scrambled symbols are, but
    domain is -5 <= x <= 5
    range is -5/3 <= y <= 5/3

    #3. Since + came out ok, I assume the equation is

    x^2 - y^2 = 16

    As you say, x- and y-axes are the axes of symmetry

    #4. If your choice is correct, the equation of the ellipse must have been

    x^2/9 + y^2/25 = 1

    #5. If your choice is correct, the equation of the hyperbola must have been

    y^2/25 - x^2 = 1

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