Chapter 10

Find the distance between each pair of points with the given coordinates. $$ (-4.3,2.6),(6.5,-3.4) $$

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ 6 x^{2}+6 y^{2}=162 $$

Find the center and radius of the circle with the given equation. Then graph the circle. $$ (x-4)^{2}+y^{2}=\frac{16}{25} $$

Write each equation in standard form. Identify the vertex, axis of symmetry, and direction of opening of the parabola. $$ y=\frac{1}{2} x^{2}+12 x-8 $$

The map of a mall is overlaid with a numeric grid. The kiosk for the cell phone store is halfway between Terry's Ice Cream and the See Clearly eyeglass store. If the ice cream store is at \((2,4)\) and the eyeglass store is at \((78,46),\) find the distance the kiosk is from the eyeglass store.

Find the exact solution(s) of each system of equations. $$ \begin{array}{l}{x^{2}+y^{2}=36} \\ {y=x+2}\end{array} $$

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ 4 x^{2}+2 y^{2}=8 $$

Write each equation in standard form. Identify the vertex, axis of symmetry, and direction of opening of the parabola. $$ x=3 y^{2}+5 y-9 $$

Find the center and radius of the circle with the given equation. Then graph the circle. $$ \left(x+\frac{2}{3}\right)^{2}+\left(y-\frac{1}{2}\right)^{2}=\frac{8}{9} $$

Find the midpoint of the line segment with endpoints at the given coordinates. $$ (8,3),(16,7) $$

Find the exact solution(s) of each system of equations. $$ \begin{array}{l}{y^{2}+x^{2}=9} \\ {y=7-x}\end{array} $$

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ x^{2}=8 y $$

Graph each equation. $$ y=-\frac{1}{6} x^{2} $$

Find the center and radius of the circle with the given equation. Then graph the circle. $$ x^{2}+y^{2}+8 x-6 y=0 $$

Find the midpoint of the line segment with endpoints at the given coordinates. $$ (-5,3),(-3,-7) $$

Find the exact solution(s) of each system of equations. $$ \begin{array}{l}{\frac{x^{2}}{30}+\frac{y^{2}}{6}=1} \\ {x=y}\end{array} $$

Write an equation for the hyperbola that satisfies each set of conditions. vertices \((-5,0)\) and \((5,0),\) conjugate axis of length 12 units

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ 4 y^{2}-x^{2}+4=0 $$

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

Find the center and radius of the circle with the given equation. Then graph the circle. $$ x^{2}+y^{2}+4 x-8=0 $$

Find the midpoint of the line segment with endpoints at the given coordinates. $$ (6,-5),(-2,-7) $$

Find the exact solution(s) of each system of equations. $$ \begin{array}{l} \frac{x^{2}}{36}-\frac{y^{2}}{4}=1 \\ x=y \end{array} $$

Write an equation for the hyperbola that satisfies each set of conditions. vertices \((0,-4)\) and \((0,4),\) conjugate axis of length 14 units

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ (x-1)^{2}-9(y-4)^{2}=36 $$

Graph each equation. $$ y=\frac{1}{3}(x+6)^{2}+3 $$

Write an equation for the ellipse that satisfies each set of conditions. endpoints of major axis at (-11, 5) and (7, 5), endpoints of minor axis at (-2, 9) and (-2, 1)

Find the midpoint of the line segment with endpoints at the given coordinates. $$ (5,9),(12,18) $$

Find the exact solution(s) of each system of equations. $$ \begin{array}{l}{4 x+y^{2}=20} \\ {4 x^{2}+y^{2}=100}\end{array} $$

Write an equation for the hyperbola that satisfies each set of conditions. vertices \((9,-3)\) and \((-5,-3),\) foci \((2 \pm \sqrt{53},-3)\)

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ y+4=(x-2)^{2} $$

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

Write an equation for the ellipse that satisfies each set of conditions. endpoints of major axis at (2, 12) and (2, -4), endpoints of minor axis at (4, 4) and (0, 4)

GEOMETRY Triangle MNP has vertices \(M(3,5), N(-2,8),\) and \(P(7,-4) .\) Find the coordinates of the midpoint of each side.

Find the exact solution(s) of each system of equations. $$ \begin{array}{l}{y+x^{2}=3} \\ {x^{2}+4 y^{2}=36}\end{array} $$

Write an equation for the hyperbola that satisfies each set of conditions. vertices \((-4,1)\) and \((-4,9),\) foci \((-4,5 \pm \sqrt{97})\)

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ (y-4)^{2}=9(x-4) $$

Graph each equation. $$ 4(x-2)=(y+3)^{2} $$

Write an equation for the ellipse that satisfies each set of conditions. major axis 20 units long and parallel to y-axis, minor axis 6 units long, center at (4, 2)

REAL ESTATE In John's town, the numbered streets and avenues form a grid. He belongs to a gym at the corner of 12 th Street and 15 th Avenue, and the deli where he works is at the corner of 4 th Street and 5th Avenue. He wants to rent an apartment halfway between the two. In what area should he look?

Find the exact solution(s) of each system of equations. $$ \begin{array}{l}{x^{2}+y^{2}=64} \\ {x^{2}+64 y^{2}=64}\end{array} $$

Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the given equation. Then graph the hyperbola. $$ \frac{x^{2}}{81}-\frac{y^{2}}{49}=1 $$

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ x^{2}+y^{2}+4 x-6 y=-4 $$

Graph each equation. $$ (y-8)^{2}=-4(x-4) $$

Write an equation for the circle that satisfies each set of conditions. center \((0,3),\) radius 7 units

At its closest point, Venus is 0.719 astronomical units from the Sun. At its farthest point, Venus is 0.728 astronomical units from the Sun. Write an equation for the orbit of Venus. Assume that the center of the orbit is the origin, the Sun lies on the \(x\)-axis, and the radius of the Sun is 400,000 miles.

Find the distance between each pair of points with the given coordinates. $$ (-4,9),(1,-3) $$

Find the exact solution(s) of each system of equations. $$ \begin{array}{l}{y^{2}+x^{2}=25} \\ {y^{2}+9 x^{2}=25}\end{array} $$

Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the given equation. Then graph the hyperbola. $$ \frac{y^{2}}{36}-\frac{x^{2}}{4}=1 $$

Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. $$ x^{2}+y^{2}+6 y+13=40 $$

Graph each equation. $$ y=x^{2}-12 x+20 $$