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Questions and Answers
What is a circle?
What is a circle?
- If $x^2$ and $y^2$ have the same coefficients (correct)
- If $x^2$ and $y^2$ do not have the same coefficients, but the same sign
- If $x^2$ and $y^2$ have opposite signs
- If only one of the two variables are squared
What is an ellipse?
What is an ellipse?
- If $x^2$ and $y^2$ do not have the same coefficients, but the same sign (correct)
- If $x^2$ and $y^2$ have the same coefficients
- If only one of the two variables are squared
- If $x^2$ and $y^2$ have opposite signs
What is a hyperbola?
What is a hyperbola?
- If $x^2$ and $y^2$ have opposite signs (correct)
- If $x^2$ and $y^2$ have the same coefficients
- If only one of the two variables are squared
- If $x^2$ and $y^2$ do not have the same coefficients, but the same sign
What is a parabola?
What is a parabola?
Find the center of the circle: $(x+8)^2+(y+3)^2=121$.
Find the center of the circle: $(x+8)^2+(y+3)^2=121$.
Find the radius of the circle: $(x-5)^2+(y+2)^2=64$.
Find the radius of the circle: $(x-5)^2+(y+2)^2=64$.
Find the domain of the circle: $(x-5)^2+(y+2)^2=64$.
Find the domain of the circle: $(x-5)^2+(y+2)^2=64$.
Find the range of the circle: $(x-5)^2+(y+2)^2=64$.
Find the range of the circle: $(x-5)^2+(y+2)^2=64$.
Find the center of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.
Find the center of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.
Find the major axis of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.
Find the major axis of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.
Find the domain of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.
Find the domain of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.
Find the range of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.
Find the range of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.
Which ways will this hyperbola open? $x^2-y^2=4$.
Which ways will this hyperbola open? $x^2-y^2=4$.
Find the center of the hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.
Find the center of the hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.
Find the domain of this hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.
Find the domain of this hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.
Find the domain of this hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.
Find the domain of this hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.
Which way will this parabola open? $2y^2+x+16y+34=0$.
Which way will this parabola open? $2y^2+x+16y+34=0$.
Find the vertex of the parabola: $y=(x+3)^2-4$.
Find the vertex of the parabola: $y=(x+3)^2-4$.
Find the domain of the parabola: $y=(x-5)^2$.
Find the domain of the parabola: $y=(x-5)^2$.
Find the range of the parabola: $y=(x-5)^2$.
Find the range of the parabola: $y=(x-5)^2$.
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Study Notes
Circle
- Defined by the equation where x² and y² have the same coefficients.
- Example center for the equation (x+8)²+(y+3)²=121 is (−8,−3).
- Radius can be determined from (x−5)²+(y+2)²=64, yielding a radius of 8.
Ellipse
- Exists when x² and y² have the same sign but different coefficients.
- Center can be found from (x-5)²/16 + (y+3)²/25 as (5,−3).
- Major axis is vertical because the larger denominator is associated with (y+3)² (25 > 16).
- Domain is [1,9] and range is [-8,2].
Hyperbola
- Created when x² and y² have opposite signs.
- For the hyperbola x²−y²=4, it opens to the left and right.
- Center retrieved from (x-5)²/16 - (y+3)²/144=1 is (5,−3).
- Domain is (-∞,1] U [9,∞) and all real numbers for the equation x-5)²/16 - (y+3)²/144=1.
Parabola
- Describes the equation with only one variable squared.
- Opens left as indicated by the equation 2y²+x+16y+34=0.
- Vertex for y=(x+3)²-4 positioned at (-3,−4).
- Domain characterized as all real numbers and range as [0,∞) for y=(x-5)².
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