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Magazine Problem 1
Classify each of the following statements as either true or false. A system of equations that represent a line and an ellipse can have \(0,1,\) or 2 solutions.
Problem 2
Match the conic section with the equation in the column on the right that represents that type of conic section. _____ A hyperbola with a vertical axis a) \(\frac{x^{2}}{10}+\frac{y^{2}}{12}=1\) b) \((x+1)^{2}+(y-3)^{2}=30\) c) \(y-x^{2}=5\) d) \(\frac{x^{2}}{9}-\frac{y^{2}}{10}=1\) e) \(x-2 y^{2}=3\) f) \(\frac{y^{2}}{20}-\frac{x^{2}}{35}=1\) g) \(3 x^{2}+3 y^{2}=75\) h) \(\frac{(x-1)^{2}}{10}+\frac{(y-4)^{2}}{8}=1\)
Problem 2
Match the equation with the center or vertex of its graph, listed in the column on the right. a) Vertex: \((-2,5)\) b) Vertex: \((5,-2)\) c) Vertex: \((2,-5)\) d) Vertex: \((-5,2)\) e) Center: \((-2,5)\) f) Center: \((2,-5)\) g) Center: \((5,-2)\) h) Center: \((-5,2)\) $$(x+2)^{2}+(y-5)^{2}=9$$
Problem 2
Classify each of the following statements as either true or false. A system of equations that represent a parabola and a circle can have up to 4 solutions.
Problem 3
Match the equation with the center or vertex of its graph, listed in the column on the right. a) Vertex: \((-2,5)\) b) Vertex: \((5,-2)\) c) Vertex: \((2,-5)\) d) Vertex: \((-5,2)\) e) Center: \((-2,5)\) f) Center: \((2,-5)\) g) Center: \((5,-2)\) h) Center: \((-5,2)\) $$(x-5)^{2}+(y+2)^{2}=9$$
Problem 3
Match the conic section with the equation in the column on the right that represents that type of conic section. _____ An ellipse with its center not at the origin a) \(\frac{x^{2}}{10}+\frac{y^{2}}{12}=1\) b) \((x+1)^{2}+(y-3)^{2}=30\) c) \(y-x^{2}=5\) d) \(\frac{x^{2}}{9}-\frac{y^{2}}{10}=1\) e) \(x-2 y^{2}=3\) f) \(\frac{y^{2}}{20}-\frac{x^{2}}{35}=1\) g) \(3 x^{2}+3 y^{2}=75\) h) \(\frac{(x-1)^{2}}{10}+\frac{(y-4)^{2}}{8}=1\)
Problem 4
Match the equation with the center or vertex of its graph, listed in the column on the right. a) Vertex: \((-2,5)\) b) Vertex: \((5,-2)\) c) Vertex: \((2,-5)\) d) Vertex: \((-5,2)\) e) Center: \((-2,5)\) f) Center: \((2,-5)\) g) Center: \((5,-2)\) h) Center: \((-5,2)\) $$(x+5)^{2}+(y-2)^{2}=9$$
Problem 4
Match the conic section with the equation in the column on the right that represents that type of conic section. _____ An ellipse with its center at the origin a) \(\frac{x^{2}}{10}+\frac{y^{2}}{12}=1\) b) \((x+1)^{2}+(y-3)^{2}=30\) c) \(y-x^{2}=5\) d) \(\frac{x^{2}}{9}-\frac{y^{2}}{10}=1\) e) \(x-2 y^{2}=3\) f) \(\frac{y^{2}}{20}-\frac{x^{2}}{35}=1\) g) \(3 x^{2}+3 y^{2}=75\) h) \(\frac{(x-1)^{2}}{10}+\frac{(y-4)^{2}}{8}=1\)
Problem 5
Match the conic section with the equation in the column on the right that represents that type of conic section. _____ A circle with its center at the origin a) \(\frac{x^{2}}{10}+\frac{y^{2}}{12}=1\) b) \((x+1)^{2}+(y-3)^{2}=30\) c) \(y-x^{2}=5\) d) \(\frac{x^{2}}{9}-\frac{y^{2}}{10}=1\) e) \(x-2 y^{2}=3\) f) \(\frac{y^{2}}{20}-\frac{x^{2}}{35}=1\) g) \(3 x^{2}+3 y^{2}=75\) h) \(\frac{(x-1)^{2}}{10}+\frac{(y-4)^{2}}{8}=1\)
Problem 5
Classify each of the following statements as either true or false. The graph of \(\frac{x^{2}}{9}+\frac{y^{2}}{25}=1\) includes the points \((-3,0)\) and \((3,0)\)
