Chapter 8

Graph each circle by hand if possible. Give the domain and range. $$x^{2}+y^{2}=36$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=t, y=\sqrt{t^{2}+2}, \text { for } t \text { in }(-\infty, \infty)$$

Determine the type of conic section represented by each equation, and graph it, provided a graph exists. $$y^{2}-4 y=x+4$$

Find an equation for each ellipse. Center \((3,-2) ; a=5 ; c=3 ;\) major axis vertical

Graph each circle by hand if possible. Give the domain and range. $$x^{2}+y^{2}=0$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=\sqrt{t}, y=t^{2}-1, \text { for } t \text { in }[0, \infty)$$

Find an equation for each ellipse. Center \((2,0) ;\) minor axis of length \(6 ;\) major axis horizontal and of length 9

Determine the type of conic section represented by each equation, and graph it, provided a graph exists. $$y^{2}-4 y=x+4\( 32. \)(x+7)^{2}+(y-5)^{2}+4=0$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=e^{t}, y=e^{-t}, \text { for } t \text { in }(-\infty, \infty)$$

Find an equation for each ellipse. Major axis of length \(6 ;\) foci \((0,2)\) and \((0,-2)\)

Determine the type of conic section represented by each equation, and graph it, provided a graph exists. $$3 x^{2}+6 x+3 y^{2}-12 y=12$$

Graph each circle by hand if possible. Give the domain and range. $$(x-2)^{2}+y^{2}=36$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=e^{2 t}, y=e^{t}, \text { for } t \text { in }(-\infty, \infty)$$

Find an equation for each ellipse. Minor axis of length \(4 ;\) foci \((-5,0)\) and \((5,0)\)

Determine the type of conic section represented by each equation, and graph it, provided a graph exists. $$-4 x^{2}+8 x+y^{2}+6 y=-6$$

Graph each circle by hand if possible. Give the domain and range. $$(x+2)^{2}+(y-5)^{2}=16$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=\frac{1}{\sqrt{t+2}}, y=\frac{t}{t+2}, \text { for } t \text { in }(-2, \infty)$$

Find an equation for each ellipse. Center \((5,2) ;\) minor axis vertical, with length \(8 ; c=3\)

Determine the type of conic section represented by each equation, and graph it, provided a graph exists. $$4 x^{2}-8 x+9 y^{2}-36 y=-4$$

Graph each circle by hand if possible. Give the domain and range. $$(x-5)^{2}+(y+4)^{2}=49$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=\frac{t}{t-1}, y=\frac{1}{\sqrt{t-1}}, \text { for } t \text { in }(1, \infty)$$

Determine the type of conic section represented by each equation, and graph it, provided a graph exists. $$3 x^{2}+12 x+3 y^{2}=0$$

Find an equation for each ellipse. Center \((-3,6) ;\) major axis vertical, with length \(10 ; c=2\)

Graph each circle by hand if possible. Give the domain and range. $$(x-4)^{2}+(y-3)^{2}=25$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) .$$x=t+2, y=\frac{1}{t+2}, \text { for } t \neq-2$$

Use the definitions of conic sections to answer the following. Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the points \((5,0)\) and \((-5,0)\) is 14.

Find an equation for each ellipse. Vertices \((4,9)\) and \((4,1) ;\) minor axis of length 6

Graph each circle by hand if possible. Give the domain and range. $$(x+3)^{2}+(y+2)^{2}=36$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=t-3, y=\frac{2}{t-3}, \text { for } t \neq 3$$

Use the definitions of conic sections to answer the following. Identify the type of conic section consisting of the set of all points in the plane for which the absolute value of the difference of the distances from the points \((3,0)\) and \((-3,0)\) is 2.

Find an equation for each ellipse. Foci at \((-3,-3)\) and \((7,-3) ;\) the point \((2,1)\) on ellipse

Graph each circle by hand if possible. Give the domain and range. $$(x-1)^{2}+(y+2)^{2}=16$$

Write the equation in standard form for an ellipse centered at ( \(h, k\) ). Identify the center and vertices. $$9 x^{2}+18 x+4 y^{2}-8 y-23=0$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=t^{2}, y=2 \ln t, \text { for } t \text { in }(0, \infty)$$

Use the definitions of conic sections to answer the following. Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point \((3,0)\) is one and one-half times the distance from the line \(x=\frac{4}{3}\).

Write the equation in standard form for an ellipse centered at ( \(h, k\) ). Identify the center and vertices. $$9 x^{2}-36 x+16 y^{2}-64 y-44=0$$

Find a rectangular equation. State the appropriate interval for \(x\) or \(y .\) $$x=\ln t, y=3 \ln t, \text { for } t \text { in }(0, \infty)$$

Use the definitions of conic sections to answer the following. Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point \((2,0)\) is one-third the distance from the line \(x=10\).

Write the equation in standard form for an ellipse centered at ( \(h, k\) ). Identify the center and vertices. $$4 x^{2}+8 x+y^{2}+2 y+1=0$$

Find the eccentricity e of each ellipse or hyperbola. $$12 x^{2}+9 y^{2}=36$$

Graph each circle using a graphing calculator. Use a square viewing window. Give the domain and range. $$x^{2}+y^{2}=81$$

Find the eccentricity e of each ellipse or hyperbola. $$8 x^{2}-y^{2}=16$$

Graph each circle using a graphing calculator. Use a square viewing window. Give the domain and range. $$x^{2}+(y+3)^{2}=49$$

Write the equation in standard form for an ellipse centered at ( \(h, k\) ). Identify the center and vertices. $$4 x^{2}+16 x+5 y^{2}-10 y+1=0$$

Find the eccentricity e of each ellipse or hyperbola. $$x^{2}-y^{2}=4$$

Graph each circle using a graphing calculator. Use a square viewing window. Give the domain and range. $$(x-3)^{2}+(y-2)^{2}=25$$

Write the equation in standard form for an ellipse centered at ( \(h, k\) ). Identify the center and vertices. $$2 x^{2}+4 x+3 y^{2}-18 y+23=0$$

Find the eccentricity e of each ellipse or hyperbola. $$x^{2}+2 y^{2}=8$$

Graph each circle using a graphing calculator. Use a square viewing window. Give the domain and range. $$(x+2)^{2}+(y+3)^{2}=36$$

Find the eccentricity e of each ellipse or hyperbola. $$4 x^{2}+7 y^{2}=28$$