Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 6
Classify each of the following statements as either true or false. The graph of \(\frac{x^{2}}{36}+\frac{y^{2}}{25}=1\) includes the points \((0,-5)\) and \((0,5)\)
Problem 6
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: \((-5,2)\) $$y=(x-5)^{2}-2$$
Problem 6
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 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 7
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: \((-5,2)\) $$x=(y-2)^{2}-5$$
Problem 7
Classify each of the following statements as either true or false. The graph of \(\frac{(x+3)^{2}}{25}+\frac{(y-2)^{2}}{36}=1\) is an ellipse centered at \((-3,2)\)
Problem 7
Match the conic section with the equation in the column on the right that represents that type of conic section. _____ A parabola opening upward or downward 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 7
Solve. Remember that graphs can be used to confirm all real solutions. $$ \begin{aligned} &x^{2}+y^{2}=25\\\ &y-x=1 \end{aligned} $$
Problem 8
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: \((-5,2)\) $$x=(y-5)^{2}-2$$
Problem 8
Classify each of the following statements as either true or false. The graph of \(\frac{(x-2)^{2}}{49}+\frac{(y+5)^{2}}{9}=1\) is an ellipse centered at \((2,-5)\)
Problem 8
Solve. Remember that graphs can be used to confirm all real solutions. $$ \begin{aligned} &x^{2}+y^{2}=100,\\\ &y-x=2 \end{aligned} $$
