Tuesday

November 25, 2014

November 25, 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......

**Answer this Question**

**Related Questions**

algebra 2 - Determine values for A, B, and C such that the equation below ...

algebra 2 - Determine values for A, B, and C such that the equation below ...

algebra help please - I notice that other problems are answered in a timely ...

pre cal - What is the center of the conic whose equation is x^2 + 2y^2 - 6x + ...

algebra - A conic section has the equation x^2+y^2+12x+8y=48. Determine the ...

math - how would you determine the eccentricity of the conic section when ...

algebra 2 - 1) In the general second-degree equation Ax^2 + Bxy + Cy^2 + Dx + Ey...

math - how would you determine the eccentricity of the conic section when ...

Algebra help! - I dont understand my problems that I am suppose to do. please ...

Math - What type of conic section is given by the equation 4x^2+9y^2=36? What ...