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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.
 

y^2 - x +5y - 25 = x^2 - 6x + 1

 Jun 23, 2022
 #1
avatar+124676 
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y^2 - x + 5y - 25 =  x^2 - 6x + 1  rewrite as

 

y^2 + 5y - x^2 + 5x  - 26 =  0 

 

-1x^2 + 0xy + 1y^2 + 5x + 5y  - 26 = 0

 

General (Standard Form) Equation Of A Conic Section

Ax^2+Bxy+Cy^2+Dx+Ey+F=0,where A,B,C,D,E,F are constants

From the standard equation, it is easy to determine the conic type eg

B^2−4AC<0 , if a conic exists, then it is a circle or ellipse

B^2−4AC=0, if a conic exists, then it is a parabola

B^2−4AC>0 , if a conic exists, it is a hyperbola

 

We have  :

 

0^2 - 4 (-1) (1)   =   4  >  0

          

 

This is a hyperbola that opens upward / downward

 

 

cool cool cool

 Jun 23, 2022
edited by CPhill  Jun 23, 2022

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