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September 23, 2014

September 23, 2014

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

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 11:35amCircle: 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 3:02pmThank you Reiny!!!! I've been asking for this as well......

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