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Determine if the graph of the equation below is a parabola, circle, ellipse, hyperbola, point, line, two lines, or empty. Enter the most specific answer.

 

x^2 + 2y^2 - 6x - 8y + 481 = 0

 Dec 12, 2020
 #1
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x^2 -2y^2  - 6x  -8y   =   -481

 

x^2 - 6x  - 2y^2 - 8y  =  -481     complete the square on  x,y

 

x^2 - 6x + 9   -  2(y^2 -4y + 4)  =  -481   + 9   -  8

 

(x - 3)^2   -2 ( y -2)^2  =  -480          divide through by 2

 

(x - 3)^2 /2  - (y - 2)^2  =   -  240      rearrange as

 

(y -2)^2   - ( x - 3)^2/2   = 240          divide  through  by   240

 

(y - 2)^2/240  - (x  - 3)^2/480  =   1

 

This is a hyperbola that  opens  up/down

 

 

cool cool cool

 Dec 12, 2020

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