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Magazine Problem 69
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 70
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 71
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 72
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 73
Use a rotation of axes to put the conic in standard position. Identify the graph, give its equation in the rotated coordinate system, and sketch the curve. $$x^{2}+x y+y^{2}=6$$
Problem 74
Use a rotation of axes to put the conic in standard position. Identify the graph, give its equation in the rotated coordinate system, and sketch the curve. $$4 x^{2}+10 x y+4 y^{2}=9$$
Problem 75
Use a rotation of axes to put the conic in standard position. Identify the graph, give its equation in the rotated coordinate system, and sketch the curve. $$4 x^{2}+6 x y-4 y^{2}=5$$
Problem 76
Use a rotation of axes to put the conic in standard position. Identify the graph, give its equation in the rotated coordinate system, and sketch the curve. $$3 x^{2}-2 x y+3 y^{2}=8$$
Problem 77
Identify the conic with the given equation and give its equation in standard form. $$3 x^{2}-4 x y+3 y^{2}-28 \sqrt{2} x+22 \sqrt{2} y+84=0$$
Problem 78
Identify the conic with the given equation and give its equation in standard form. $$6 x^{2}-4 x y+9 y^{2}-20 x-10 y-5=0$$
