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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 + 21 = 0

 Nov 30, 2020
 #1
avatar+114592 
+2

x^2 + 2y^2   - 6x   - 8y  + 21  = 0    complete the square on x, y

 

(x^2 -6x  + 9 ) +  2(y^2 - 4y  + 4)  =  -21 + 9 + 8

 

( x - 3)^2  + 2 ( y - 2)^2  = -4     

 

This is empty......both  squared quantities  added together will have a minimum of  0  when (x,y)= ( 3,2)

And this sum will never =   -4

 

cool cool cool

 Nov 30, 2020
edited by CPhill  Nov 30, 2020

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