Algebra II

posted by .

I am lost on this one!!!
Determine values for A, B, and C such that the equation below represents the
given type of conic. Each axis of the ellipse, parabola, and hyperbola should
be horizontal or vertical. Then rewrite your equation for each conic in standard
form, identify (h, k), and describe the translation. Part A: Circle, Part B: Ellipse,
Part C: Parabola, Part D: Hyperbola
Ax^2+Bxy+Cy^2+2x-4y-5=0

  • Algebra II -

    Circle: A = 1 , C = 1 , B = 0
    x^2 + 2x + y^2 - 4y = 5
    x^2 + 2x + 1 + y^2 - 4y + 4 = 5+1+4
    (x+1)^2 + (y-2)^2 = 10
    circle: centre(-1,2) and radius √10

    Ellipse : A=1, C=2, B=0
    x^2 + 2x + 2(y^2 - 2y ) = 5
    x^2 + 2x + 1 + 2(y^2 - 2y + 1) = 5 + 1 + 2
    (x+1)^2 + 2(y-1)^2 = 8
    divide by 8
    (x+1)^2 /8 + (y-1)^2 /4 = 1

    Parabola:
    let A=1, C=0, B=0
    x^2 + 2x - 5 = 4y
    4y = x^2 + 2x + 1 - 1 - 5
    4y = (x+1)^2 - 6
    y = (1/4)(x+1)^2 - 3/2

    hyperbola:
    let A=1, B=0, C=-1
    x^2 + 2x - (y^2 + 2y) = 5
    (x^2 + 2x + 1) - (y^2 + 2y + 1) = 5 + 1 - 1
    (x+1)^2 - (y+1)^2 = 5

    (x+1)^2 /5 - (y+1)^2 /5 = 1

    Since you wanted all axes to be either vertical or horizontal, the xy term cannot be there, so in all cases B = 0

  • Algebra II -

    Thank you Reiny!!!! I've been asking for this as well......

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    how would you determine the eccentricity of the conic section when represented by the equation ax^2+cy^2+dx+ey+f=0 if the equation represents an ellipse and then when it represents a hyperbola.please help.
  2. pre-calculus

    How do i know if a conic section is a circle, ellipse, hyperbola, or parabola?
  3. pre cal

    What is the center of the conic whose equation is x^2 + 2y^2 - 6x + 8y = 0 2.Which one of the following equations represents a hyperbola?
  4. algebra 2

    Determine values for A, B, and C such that the equation below represents the given type of conic. Each axis of the ellipse, parabola, and hyperbola should be horizontal or vertical. Then rewrite your equation for each conic in standard …
  5. algebra 2

    Determine values for A, B, and C such that the equation below represents the given type of conic. Each axis of the ellipse, parabola, and hyperbola should be horizontal or vertical. Then rewrite your equation for each conic in standard …
  6. algebra help please

    I notice that other problems are answered in a timely manner....was is my overlooked?
  7. precalculus

    Given: r = 4/-2-6sintheta What type of conic does this represent?
  8. precalculus

    Can you please check and correct my answers?
  9. precalculus

    Given: r = 4/-2-costheta What type of conic does this represent?
  10. Algebra

    Write the equation for the conic section of the cone is centered at (0,0), the major axis is 10 units and the minor axis is 6 units. (Ellipse) Write the equation for the conic section if the vertex is (-6,4) and the focus is (-6,7) …

More Similar Questions