The graph of 50x^{2}-50x+200y+(409/2)+50y^{2}=0 is a

circle

parabola

ellipse

hyperbola

50x^{2}-50x+200y+(409/2)+50y^{2}=0

50x^{2}+50y^{2}-50x+200y+(409/2) =0

The graph of Ax^{2}+Cy^{2}+Dx+Ey+F=0, when A=C (in this case 50=50) is a circle.