algebra
posted by Lee .
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 yaxis and the xaxis are lines of symmetry.( my choice)
Every line through the center is a line of symmetry.
The yaxis and the xaxis 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 xaxis, the yaxis, y = x, and y = ¨Cx.
Every line through the center is a line of symmetry.
It has four lines of symmetry, the xaxis, the yaxis, y = x, and y = ¨Cx.
It has two lines of symmetry, the xaxis and the yaxis. ( 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 xintercepts are (0, 5) and (0, ¨C5).
The yintercepts 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 xintercepts are (¨C3, 0) and (3, 0).
The yintercepts 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 xintercepts are (0, 5) and (0, ¨C5).
The yintercepts 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 xintercepts are (0, 5) and (0, ¨C5).
The yintercepts 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 yintercepts 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 xintercepts 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 yintercepts 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 xintercepts are (0, 5) and (0, ¨C5).
The domain is all real numbers.
The range is {x  x ¡Ü ¨C5 or x ¡Ý 5}.

#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 yaxes 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 
12m to the 3rd power plus 12m to the 2nd power plus 0m divided by 3m to the 2ns power divided by 3m to the 2nd power

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Thanks^^ 100% right

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