Algebra 2 - Conic Sections Flashcards
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Questions and Answers

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?

  • 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?

  • 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?

    <p>If only one of the two variables is squared</p> Signup and view all the answers

    Find the center of the circle: $(x+8)^2+(y+3)^2=121$.

    <p>(-8, -3)</p> Signup and view all the answers

    Find the radius of the circle: $(x-5)^2+(y+2)^2=64$.

    <p>8</p> Signup and view all the answers

    Find the domain of the circle: $(x-5)^2+(y+2)^2=64$.

    <p>[-3, 13]</p> Signup and view all the answers

    Find the range of the circle: $(x-5)^2+(y+2)^2=64$.

    <p>[-10, 6]</p> Signup and view all the answers

    Find the center of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.

    <p>(5, -3)</p> Signup and view all the answers

    Find the major axis of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.

    <p>Vertical</p> Signup and view all the answers

    Find the domain of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.

    <p>[1, 9]</p> Signup and view all the answers

    Find the range of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.

    <p>[-8, 2]</p> Signup and view all the answers

    Which ways will this hyperbola open? $x^2-y^2=4$.

    <p>Left/right</p> Signup and view all the answers

    Find the center of the hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.

    <p>(5, -3)</p> Signup and view all the answers

    Find the domain of this hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.

    <p>(-infinity, 1] U [9, infinity)</p> Signup and view all the answers

    Find the domain of this hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.

    <p>All real numbers</p> Signup and view all the answers

    Which way will this parabola open? $2y^2+x+16y+34=0$.

    <p>Left</p> Signup and view all the answers

    Find the vertex of the parabola: $y=(x+3)^2-4$.

    <p>(-3, -4)</p> Signup and view all the answers

    Find the domain of the parabola: $y=(x-5)^2$.

    <p>All real numbers</p> Signup and view all the answers

    Find the range of the parabola: $y=(x-5)^2$.

    <p>[0, infinity)</p> Signup and view all the answers

    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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    Test your knowledge of conic sections in Algebra 2 with these flashcards. Each card defines key terms such as circle, ellipse, hyperbola, and parabola. Perfect for studying or quick reviews before exams.

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