+21 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
+100 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
+100 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
