Chapter 22

Find the slope and the \(y\) intercept for each equation, and make a graph. $$y=7 x+2$$

Find the center and radius of each circle. Graph. $$(x-2.22)^{2}+(y+7.16)^{2}=5.93$$

Find the vertex, focus, focal width, and equation of the axis for each parabola. Make a graph. $$(y+3)^{2}=4(x+5)$$

Length of a Line Segment Find the length of the line segment with the given endpoints. (-2,0) and (7,0)

Find the slope and the \(y\) intercept for each equation, and make a graph. $$y=-\frac{1}{2} x-\frac{1}{4}$$

Rewrite each standard equation in general form. $$(x+2)^{2}+(y+3)^{2}=16$$

Length of a Line Segment Find the length of the line segment with the given endpoints. (-4,0) and (-6,0)

Write the equation of each ellipse in standard form. Distance between foci \(=18 ;\) sum of axes \(=54 ;\) horizontal major axis.

Find the slope and the \(y\) intercept for each equation, and make a graph. $$y=-3 x+2$$

Rewrite each standard equation in general form. $$(x+3)^{2}+(y-5)^{2}=25$$

Length of a Line Segment Find the length of the line segment with the given endpoints. (0,-2.74) and (0,3.86)

Find the center, lengths of the semiaxes, foci, slope of the asymptotes, and vertices for each hyperbola. Graph some $$\frac{(x-2)^{2}}{25}-\frac{(y+1)^{2}}{16}=1$$

Find the coordinates of the center, vertices, and foci for each ellipse. Round to three significant digits where needed.$$\frac{(x-2)^{2}}{16}+\frac{(y+2)^{2}}{9}=1$$

Write the equation of each line in slope-intercept form. Slope \(=2 ;\) passes through (3,4)

Rewrite each standard equation in general form. $$(x-5)^{2}+(y+4)^{2}=42$$

Length of a Line Segment Find the length of the line segment with the given endpoints. (55.34,0) and (25.38,0)

Find the center, lengths of the semiaxes, foci, slope of the asymptotes, and vertices for each hyperbola. Graph some $$\frac{(y+3)^{2}}{25}-\frac{(x-2)^{2}}{49}=1$$

Find the coordinates of the center, vertices, and foci for each ellipse. Round to three significant digits where needed.$$\frac{(x+5)^{2}}{25}+\frac{(y-3)^{2}}{49}=1$$

Write the equation of each line in slope-intercept form. Slope \(=3 ;\) passes through (2,5)

Rewrite each standard equation in general form. $$(x-7)^{2}+(y-8)^{2}=38$$

Find the vertex, focus, focal width, and equation of the axis for each parabola. Make a graph. $$x^{2}+4 x-y-6=0$$

Length of a Line Segment Find the length of the line segment with the given endpoints. (5.59,3.25) and (8.93,3.25)

Write the equation of each line in general form. Slope \(=-4 ;\) passes through (-2,5)

Rewrite each general equation in standard form. Find the center and radius. Graph. $$x^{2}+y^{2}-8 x=0$$

Write the equation of each parabola in standard form. Find all missing features and graph. vertex at (1,2)\(; L=8 ;\) axis is \(y=2 ;\) opens to the right

Length of a Line Segment Find the length of the line segment with the given endpoints. (-2.06,-5.83) and (-2.06,-8.34)

Write the equation of each line in general form. Slope \(=-2 ;\) passes through (-2,-3)

Rewrite each general equation in standard form. Find the center and radius. Graph. $$x^{2}+y^{2}-2 x-4 y=0$$

Length of a Line Segment Find the length of the line segment with the given endpoints. (8.38,-3.95) and (2.25,-4.99)

Write the equation of each line in general form. \(y\) intercept \(=3 ;\) parallel to \(y=5 x-2\)

Rewrite each general equation in standard form. Find the center and radius. Graph. $$x^{2}+y^{2}-10 x+12 y+25=0$$

Write the equation of each parabola in standard form. Find all missing features and graph. vertex (0,2)\(;\) axis is \(x=0 ;\) passes through (-4,-2)

Slope Find the slope of each straight line. Rise \(=4 ;\) run \(=2\)

Write the equation of each hyperbola in standard form. length of the conjugate axis \(=8\) and is horizontal; center at (-1,-1)\(;\) length of the transverse axis \(=16\)

Write the equation of each line in general form. \(y\) intercept \(=-2.3 ;\) parallel to \(2 x-3 y+1=0\)

Rewrite each general equation in standard form. Find the center and radius. Graph. $$x^{2}+y^{2}-4 x+2 y=36$$

Rewrite standard equation in general form. $$(x+3)^{2}=2(y+2)$$

Slope Find the slope of each straight line. Rise \(=6 ;\) run \(=4\)

Write the equation of each hyperbola in standard form. $$\frac{x^{2}}{25}-\frac{y^{2}}{9}=1$$

Write the equation of each line in general form. \(y\) intercept \(=-5 ;\) perpendicular to \(y=3 x-4\)

Rewrite each general equation in standard form. Find the center and radius. Graph. $$x^{2}+y^{2}+6 x-2 y=15$$

Rewrite standard equation in general form. $$(x+6)^{2}=4(y-5)$$

Slope Find the slope of each straight line. Rise \(=-4 ;\) run \(=4\)

Write each standard equation in general form. $$\frac{x^{2}}{16}-\frac{y^{2}}{36}=4$$

Write the equation of each line in general form. \(y\) intercept \(=2 ;\) perpendicular to \(4 x-3 y=7\)

Rewrite each general equation in standard form. Find the center and radius. Graph. $$x^{2}+y^{2}-2 x-6 y=39$$

Rewrite standard equation in general form. $$(y+7)^{2}=3(x-2)$$

Slope Find the slope of each straight line. Rise \(=-9 ;\) run \(=-3\)

Write the equation of each ellipse.Center at (0,3)\(;\) vertical major axis \(=12 ;\) length of minor axis \(=6\).

Write the equation of each line in general form. passes through (-2,5)\(;\) parallel to \(y=5 x-1\)