Honors Algebra 2: Assignment 74 Unit Review

Calculator inactive

  1. Write the equation for the parabola with focus \((3, 2)\) and directrix \(y = -1.\)
    2. Solution

    \( \displaystyle y = \frac{1}{6}\left(x - 3\right)^2 + \frac{1}{2}\)

  2. Graph \(x = 5(y + 3)^2 + 7.\) Give the coordinates of the vertex and the equation of the axis of symmetry.
    3. Solution

    A parabola opening right. Vertex at \((7, -3),\) axis of symmetry \(y = -3.\)

  3. Find the equation of a parabola determined by vertex \((0, 0)\) and focus \((3, 0).\)
    4. Solution

    \( \displaystyle x = \frac{1}{12}y^2\)

  4. Find an equation of the ellipse with \( \displaystyle \left(0, \pm \sqrt{3}\right) \)as foci and 4 as the sum of the focal radii.
    5. Solution

    \( \displaystyle x^2 + \frac{y^2}{4} = 1\)

  5. Graph \(9x^2 + 49y^2 = 441.\) Give the x- and y-intercepts. Find the coordinates of the foci.
    6. Solution

    A horizontal ellipse centered at the origin with x-intercepts \(( \pm 7, 0)\) and y-intercepts \((0, \pm3).\) The foci are \( \displaystyle \left( \pm 2\sqrt{10}, 0\right).\)

  6. Sketch the graph and label the coordinates of the foci and vertices:\( 9x^2 - 4y^2 - 18x + 16y - 43 = 0.\)
    7. Solution

    A horizontal hyperbola with center \((1, 2),\) vertices \((-1, 2)\) and \((3, 2),\) and foci \((1 \pm \sqrt{13}, 2)\)

  7. Sketch the graph and label the coordinates of the foci and vertices: \(y^2 - 9x^2 - 36x - 45 = 0.\)
    8. Solution

    A vertical hyperbola with center \((-2, 0),\) vertices \((-2, \pm 3),\) and foci \((-2, \pm \sqrt{10}).\)

  8. Find an equation of the hyperbola with foci at \( (\pm 5, 0)\) and asymptotes \( \displaystyle y = \pm \frac{2}{3}x.\)
    9. Solution

    \( \displaystyle \frac{x^2}{\frac{225}{13}} - \frac{y^2}{\frac{100}{13}} = 1.\)

  9. Determine an equation of the form \(x^2 + y^2 + ax + by + c = 0\) for the circle with center \((-1, 5)\) and passing through the point \((-1, 8).\)
    10. Solution

    \(x^2 + y^2 + 2x - 10y + 17 = 0.\)

  10. Sketch the graph of the inequality \(x^2 + y^2 > 6x.\)
    11. Solution

    This is a dotted circle with center \((3, 0)\) and radius 3 shaded outside.

  11. Identify the following as circle, parabola, ellipse, or hyperbola: \(x^2 + y^2 - 8x + 2y = -8.\)
    12. Solution

    circle

  12. Identify the following as circle, parabola, ellipse, or hyperbola: \(x^2 = 8y.\)
    13. Solution

    parabola

  13. Identify the following as circle, parabola, ellipse, or hyperbola: \(36x^2 - 4y^2 - 144 = 0.\)
    14. Solution

    hyperbola

  14. Identify the following as circle, parabola, ellipse, or hyperbola: \(x^2 + 4y^2 - 16 = 0.\)
    15. Solution

    ellipse

  15. Identify the following as circle, parabola, ellipse, or hyperbola: \(x + 2y^2 - 8y + 4 = 0.\)
    16. Solution

    parabola