Homework Help: Algebra II

Posted by Jared on Monday, May 28, 2012 at 10:19am.

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 - Reiny, Monday, May 28, 2012 at 11:35am
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 - jenny, Monday, May 28, 2012 at 3:02pm
Thank you Reiny!!!! I've been asking for this as well......

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