Chapter 10

Write an equation of an ellipse in standard form with center at the origin and with the given vertex and co-vertex. $$ (4,0),(0,3) $$

Write an equation of an ellipse with the given characteristics. Check your answers. center \((-2,1),\) horizontal major axis of length \(6,\) minor axis of length 4

Graph each equation. $$ \frac{x^{2}}{16}-\frac{y^{2}}{4}=1 $$

Write an equation for a graph that is the set of all points in the plane that are equidistant from the given point and the given line. $$ F(0,2), y=-2 $$

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range. $$ 3 y^{2}-x^{2}=25 $$

Write an equation of a circle with the given center and radius. Check your answers. $$ (0,0), 10 $$

Write an equation of an ellipse in standard form with center at the origin and with the given vertex and co-vertex. $$ (0,1),(2,0) $$

Write an equation of an ellipse with the given characteristics. Check your answers. center \((5,3),\) vertical major axis of length \(12,\) minor axis of length 8

Graph each equation. $$ \frac{y^{2}}{169}-\frac{x^{2}}{16}=1 $$

Write an equation for a graph that is the set of all points in the plane that are equidistant from the given point and the given line. $$ F(0,-1), y=1 $$

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range. $$ 2 x^{2}+y^{2}=36 $$

Write an equation of a circle with the given center and radius. Check your answers. $$ (-4,-6), 7 $$

Write an equation of an ellipse in standard form with center at the origin and with the given vertex and co-vertex. $$ (3,0),(0,-1) $$

Write an equation of an ellipse with the given characteristics. Check your answers. center \((0,-4),\) horizontal major axis of length \(12,\) minor axis of length 10

Write an equation for a graph that is the set of all points in the plane that are equidistant from the given point and the given line. $$ F(-3,0), x=3 $$

Graph each equation. $$ \frac{x^{2}}{25}-\frac{y^{2}}{36}=1 $$

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range. $$ x^{2}+y^{2}=16 $$

Write an equation of a circle with the given center and radius. Check your answers. $$ (2,3), 4.5 $$

Write an equation of an ellipse in standard form with center at the origin and with the given vertex and co-vertex. $$ (0,6),(1,0) $$

Write an equation of an ellipse with the given characteristics. Check your answers. center \((3,-6),\) vertical major axis of length \(14,\) minor axis of length 6

Write an equation for a graph that is the set of all points in the plane that are equidistant from the given point and the given line. $$ F(0,-8), y=8 $$

Graph each equation. $$ x^{2}-4 y^{2}=4 $$

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range. $$ 3 y^{2}-x^{2}=9 $$

Write an equation of a circle with the given center and radius. Check your answers. $$ (-6,10), 1 $$

Write an equation of an ellipse in standard form with center at the origin and with the given vertex and co-vertex. $$ (0,-7),(4,0) $$

Write an equation of a hyperbola with the given characteristics. vertices \((1,-3)\) and \((-7,-3),\) foci \((2,-3)\) and \((-8,-3)\)

Graph each equation. $$ 36 y^{2}-9 x^{2}=324 $$

Write an equation for a graph that is the set of all points in the plane that are equidistant from the given point and the given line. $$ F(0,4), y=0 $$

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range. $$ 4 x^{2}+25 y^{2}=100 $$

Write an equation of a circle with the given center and radius. Check your answers. $$ (1,-3), 10 $$

Write an equation of an ellipse in standard form with center at the origin and with the given vertex and co-vertex. $$ (-6,0),(0,5) $$

Write an equation of a hyperbola with the given characteristics. vertices \((4,-1)\) and \((4,-5),\) foci \((4,3)\) and \((4,-9)\)

Graph each equation. $$ 25 x^{2}-16 y^{2}=400 $$

Write an equation for a graph that is the set of all points in the plane that are equidistant from the given point and the given line. $$ F\left(\frac{1}{2}, 0\right), x=-\frac{1}{2} $$

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range. $$ x^{2}+y^{2}=49 $$

Write an equation of a circle with the given center and radius. Check your answers. $$ (-5,-1), 6 $$

Write an equation of an ellipse in standard form with center at the origin and with the given vertex and co-vertex. $$ (-9,0),(0,-2) $$

Write an equation of a hyperbola with the given characteristics. vertices \((2,2)\) and \((-4,2),\) foci \((6,2)\) and \((-8,2)\)

Graph each equation. $$ 9 x^{2}-49 y^{2}=441 $$

Write an equation of a parabola with a vertex at the origin and the given focus. focus at \((6,0)\)

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range. $$ x^{2}-y^{2}+1=0 $$

Write an equation of a circle with the given center and radius. Check your answers. $$ (-3,0), 8 $$

Write an equation of an ellipse in standard form with center at the origin and with the given vertex and co-vertex. $$ (0,5),(-3,0) $$

Write an equation of a hyperbola with the given characteristics. vertices \((-1,4)\) and \((-1,-6),\) foci \((-1,8)\) and \((-1,-10)\)

Graph each equation. $$ 25 x^{2}-35 y^{2}=875 $$

Write an equation of a parabola with a vertex at the origin and the given focus. focus at \((0,-4)\)

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range. $$ x^{2}-2 y^{2}=4 $$

Write an equation of a circle with the given center and radius. Check your answers. $$ (-1.5,-3), 2 $$

Find an equation of an ellipse for each given height and width. Assume that the center of the ellipse is \((0,0) .\) $$ h=1 \mathrm{m}, w=3 \mathrm{m} $$

Write an equation of a hyperbola with the given characteristics. vertices \((0,-2)\) and \((0,4),\) foci \((0,6)\) and \((0,-4)\)