Chapter 22

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

Find the coordinates of the vertices and foci for each ellipse.$$\cdot \frac{x^{2}}{25}+\frac{y^{2}}{16}=1$$

Write the equation of each circle in standard form. Graph. center at (0,0)\(;\) radius \(=7\)

Find the coordinates of the focal point and the focal width for parabola. Graph. $$y^{2}=8 x$$

Write the equation of each straight line in slope-intercept form, and make a graph. Slope \(=4 ; y\) intercept \(=-3\)

Directed Distance Find the directed distance \(A B\). $$A(3,0) ; B(5,0)$$

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

Find the coordinates of the vertices and foci for each ellipse.$$\frac{x^{2}}{49}+\frac{y^{2}}{36}=1$$

Write the equation of each circle in standard form. Graph. center at (0,0)\(;\) radius \(=4.82\)

Find the coordinates of the focal point and the focal width for parabola. Graph. $$x^{2}=16 y$$

Write the equation of each straight line in slope-intercept form, and make a graph.. Slope \(=-1 ; y\) intercept \(=2\)

Directed Distance Find the directed distance \(A B\). $$B(-6,-6) ; A(-6,-7)$$

Find the vertices, the foci, the lengths \(a\) and \(b\) of the semiaxes, and the slope of the asymptotes for each hyperbola. Graph some. $$16 x^{2}-9 y^{2}=144$$

Find the coordinates of the vertices and foci for each ellipse.$$3 x^{2}+4 y^{2}=12$$

Write the equation of each circle in standard form. Graph. center at (2,3)\(;\) radius \(=5\)

Write the equation of each straight line in slope-intercept form, and make a graph. Slope \(=3 ; y\) intercept \(=-1\)

Directed Distance Find the directed distance \(A B\). $$B(-8,-2) ; A(-8,-5)$$

Find the vertices, the foci, the lengths \(a\) and \(b\) of the semiaxes, and the slope of the asymptotes for each hyperbola. Graph some. $$9 x^{2}-16 y^{2}=144$$

Find the coordinates of the vertices and foci for each ellipse.$$64 x^{2}+15 y^{2}=960$$

Write the equation of each circle in standard form. Graph. center at (5,2)\(;\) radius \(=10\)

Write the equation of each straight line in slope-intercept form, and make a graph. Slope \(=-2 ; y\) intercept \(=3\)

Directed Distance Find the directed distance \(A B\). $$A(-9,-2) ; B(17,-2)$$

Find the vertices, the foci, the lengths \(a\) and \(b\) of the semiaxes, and the slope of the asymptotes for each hyperbola. Graph some. $$x^{2}-4 y^{2}=16$$

Find the coordinates of the vertices and foci for each ellipse.$$4 x^{2}+3 y^{2}=48$$

Write the equation of each circle in standard form. Graph. center at \((5-3) \cdot\) radius \(=4\)

Write the equation of each straight line in slope-intercept form, and make a graph. Slope \(=2.3 ; y\) intercept \(=-1.5\)

Directed Distance Find the directed distance \(A B\). $$A(3.95,-2.07) ; B(-3.95,-2.07)$$

Find the vertices, the foci, the lengths \(a\) and \(b\) of the semiaxes, and the slope of the asymptotes for each hyperbola. Graph some. $$3 x^{2}-y^{2}+3=0$$

Find the coordinates of the vertices and foci for each ellipse.$$8 x^{2}+25 y^{2}=200$$

Write the equation of each circle in standard form. Graph. center at (-3,-2)\(;\) radius \(=11\)

Write the equation of each straight line in slope-intercept form, and make a graph. Slope \(=-1.5 ; y\) intercept \(=3.7\)

Directed Distance Find the directed distance \(A B\). $$B(11.5,3.68) ; A(11.5,-5.38)$$

Increments A particle moves from point \(A\) to point \(B\). Find the increments \(\Delta x\) and \(\Delta y\) in its coordinates. $$A(2,4), B(5,7)$$

Write the equation of each hyperbola in standard form. vertices at (±5,0)\(;\) foci at (±13,0)

Write the equation of each ellipse in standard form.Vertices at (±5,0)\(;\) foci at (±4,0).

Find the center and radius of each circle. Graph. $$x^{2}+y^{2}=49$$

Increments A particle moves from point \(A\) to point \(B\). Find the increments \(\Delta x\) and \(\Delta y\) in its coordinates. $$A(3,6), B(6,4)$$

Write the equation of each hyperbola in standard form. vertices at (0,±7)\(;\) foci at (0,±10)

Find the center and radius of each circle. Graph. $$x^{2}+y^{2}=64.8$$

Increments A particle moves from point \(A\) to point \(B\). Find the increments \(\Delta x\) and \(\Delta y\) in its coordinates. $$A(-4,4), B(5,-8)$$

Find the center and radius of each circle. Graph. $$(x-2)^{2}+(y+4)^{2}=16$$

Find the vertex, focus, focal width, and equation of the axis for each parabola. Make a graph. $$(y-5)^{2}=12(x-3)$$

Increments A particle moves from point \(A\) to point \(B\). Find the increments \(\Delta x\) and \(\Delta y\) in its coordinates. $$A(-9,-5), B(-3,-8)$$

Find the center and radius of each circle. Graph. $$(x+5)^{2}+(y-2)^{2}=49$$

Find the vertex, focus, focal width, and equation of the axis for each parabola. Make a graph. $$(x+2)^{2}=16(y-6)$$

Length of a Line Segment Find the length of the line segment with the given endpoints. (5,0) and (2,0)

Find the slope and the \(y\) intercept for each equation, and make a graph. $$y=3 x-5$$

Find the center and radius of each circle. Graph. $$(y+5)^{2}+(x-3)^{2}=36$$

Find the vertex, focus, focal width, and equation of the axis for each parabola. Make a graph. $$(x-3)^{2}=24(y+1)$$

Length of a Line Segment Find the length of the line segment with the given endpoints. (0,3) and (0,-5)