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Magazine Problem 44
Identify the graph of the given equation. $$x=-2 y^{2}$$
Problem 45
Use a translation of axes to put the conic in standard position. Identify the graph, give its equation in the translated coordinate system, and sketch the curve. $$x^{2}+y^{2}-4 x-4 y+4=0$$
Problem 46
Use a translation of axes to put the conic in standard position. Identify the graph, give its equation in the translated coordinate system, and sketch the curve. $$4 x^{2}+2 y^{2}-8 x+12 y+6=0$$
Problem 47
Use a translation of axes to put the conic in standard position. Identify the graph, give its equation in the translated coordinate system, and sketch the curve. $$9 x^{2}-4 y^{2}-4 y=37$$
Problem 48
Use a translation of axes to put the conic in standard position. Identify the graph, give its equation in the translated coordinate system, and sketch the curve. $$x^{2}+10 x-3 y=-13$$
Problem 49
Use a translation of axes to put the conic in standard position. Identify the graph, give its equation in the translated coordinate system, and sketch the curve. $$2 y^{2}+4 x+8 y=0$$
Problem 50
Use a translation of axes to put the conic in standard position. Identify the graph, give its equation in the translated coordinate system, and sketch the curve. $$2 y^{2}-3 x^{2}-18 x-20 y+11=0$$
Problem 51
Use a translation of axes to put the conic in standard position. Identify the graph, give its equation in the translated coordinate system, and sketch the curve. $$x^{2}+x y+y^{2}=6$$
Problem 52
Use a translation of axes to put the conic in standard position. Identify the graph, give its equation in the translated coordinate system, and sketch the curve. $$4 x^{2}+10 x y+4 y^{2}=9$$
Problem 53
Use a translation of axes to put the conic in standard position. Identify the graph, give its equation in the translated coordinate system, and sketch the curve. $$4 x^{2}+6 x y-4 y^{2}=5$$
