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Suppose that the graph of 2x^2+y^2+8x-10y+c=0 consists of a single point. (In this case, we call the graph a degenerate ellipse.) Find c

 Dec 30, 2019

Best Answer 

 #1
avatar+98 
+2

We try to rewrite the given equation in the standard form for an ellipse. Completing the square in both variables, we have

2(x^2+4x) + (y^2-10y) + c = 0

2(x^2+4x+4) + (y^2-10y+25) + c = 33

2(x+2)^2 + (y-5)^2 = 33-c

we need 2(x+2)^2 + (y-5)^2 to be 0 (degenerate ellipse)

so c=33

 Dec 30, 2019
 #1
avatar+98 
+2
Best Answer

We try to rewrite the given equation in the standard form for an ellipse. Completing the square in both variables, we have

2(x^2+4x) + (y^2-10y) + c = 0

2(x^2+4x+4) + (y^2-10y+25) + c = 33

2(x+2)^2 + (y-5)^2 = 33-c

we need 2(x+2)^2 + (y-5)^2 to be 0 (degenerate ellipse)

so c=33

Atroshus Dec 30, 2019
 #2
avatar+109563 
0

Very nice, Atroshus   !!!!

 

 

cool cool cool

CPhill  Dec 30, 2019

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