Friday

April 18, 2014

April 18, 2014

Posted by **Sharon** on Sunday, May 27, 2012 at 5:46pm.

- Algebra II -
**jenny**, Sunday, May 27, 2012 at 6:31pmHyperbola (x-2)^2-4(y-1)^2=36

I have that one on my exam too.

- Algebra II -
**Bosnian**, Sunday, May 27, 2012 at 7:53pmThe General Equation for a Conic Sections:

A x ^ 2 + B x y + C y ^ 2 + D x + E y + F = 0

In this case:

x ^ 2 - 4 y ^ 2 - 4 x - 8 y = 36 Subtract 36 to both sides

x ^ 2 - 4 y ^ 2 - 4 x - 8 y - 36 = 0

1 * x ^ 2 + 0 * B x y - 4 * y ^ 2 - 4 * x - 8 * y - 36 = 0

A = 1

B = 0

C = - 4

D = - 4

E = - 8

F = - 36

The discriminant B ^ 2 - 4 A C will identify which conic section it is.

If the discriminant is positive, the section is a hyperbola.

If it is negative, the section is an ellipse.

If it is zero, the section is a parabola.

B ^ 2 - 4 A C = 0 ^ 2 - 4 * 1 * ( - 4 ) = 0 + 16 = 16

The discriminant is positive.

Your line is a hyperbola.

Equation of hyperbola in standard form :

( x - h ) ^ 2 / a ^ 2 - ( y - k ) ^ 2 / b ^ 2 = 1

x ^ 2 - 4 y ^ 2 - 4 x - 8 y = 36

x ^ 2 - 4 x - 4 y ^ 2 - 8 y = 36

( x ^ 2 - 4 x ) - 4 ( y ^ 2 + 2 y ) = 36

The process involves completing the square separately for the x and y variables.

____________________________________

( x - 2 ) ^ 2 = x ^ 2 - 2 * x * 2 + 2 ^ 2

( x - 2 ) ^ 2 = x ^ 2 - 4 x + 4 Subtract 4 to both sides

( x - 2 ) ^ 2 - 4 = x ^ 2 - 4 x + 4 - 4

( x - 2 ) ^ 2 - 4 = x ^ 2 - 4 x

x ^ 2 - 4 x = ( x - 2 ) ^ 2 - 4

( y + 1 ) ^ 2 = y ^ 2 + 2 * y * 1 + 1 ^ 2

( y + 1 ) ^ 2 = y ^ 2 + 2 y + 1 Subtract 1 to both sides

( y + 1 ) ^ 2 - 1 = y ^ 2 + 2 y + 1 - 1

( y + 1 ) ^ 2 - 1 = y ^ 2 + 2 y

y ^ 2 + 2 y = ( y + 1 ) ^ 2 - 1

- 4 * ( y ^ 2 + 2 y ) = - 4 * [ ( y + 1 ) ^ 2 - 1 ]

- 4 * ( y ^ 2 + 2 y ) = - 4 ( y + 1 ) ^ 2 + 4

__________________________

x ^ 2 - 4 x - 4 y ^ 2 - 8 y = 36

x ^ 2 - 4 x - 4 ( y ^ 2 + 2 y ) = 36

( x ^ 2 - 4 x ) - 4 ( y ^ 2 + 2 y ) = 36

( x - 2 ) ^ 2 - 4 - 4 ( y + 1 ) ^ 2 + 4 = 36

( x - 2 ) ^ 2 - 4 ( y + 1 ) ^ 2 = 36 Divide both sides by 36

( x - 2 ) ^ 2 / 36 - 4 ( y + 1 ) ^ 2 / 36 = 1

( x - 2 ) ^ 2 / 36 - 4 ( y + 1 ) ^ 2 / ( 4 * 9 ) = 1

( x - 2 ) ^ 2 / 36 - ( y + 1 ) ^ 2 / 9 = 1

**Related Questions**

Algebra - Which is the equation in standard form of the line that is ...

Math - I am trying to find the standard form of this equation for an ellipse. ...

Math(Please check) - I am trying to find the standard form of this equation for ...

Algebra II - Write 36x^2-360x-25y^2-100y=100 in standard form. Then state ...

algebra - 4)Write the equation x^2-2x+y^2+4y=11 in standard form. answer= (x-1)^...

Algebra HELP - USE LINEAR COMBINATIONS TO SOLVE THE SYSTEM OF LINEAR EQUATIONS (...

algebra - 1)Write an equation for an ellipse if the endpoints of the major axis ...

Algebra-Please check work - I've reworked this and added on is any of it correct...

Math.... again......!!!!!!... - A fraction is equivelant to 4/5. The sum of the ...

Algebra II - Write y=x^2+4x-1 in vertex form. y=x^2+4x-1 y=(x^2+4x+8)-1-8 y=(x+2...