Chapter 13

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ \frac{x^{2}}{4}+\frac{y^{2}}{1}=1 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ y^{2}=8 x $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ \frac{x^{2}}{16}+\frac{y^{2}}{1}=1 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ y^{2}=-4 x $$

For Problems 1-14, write the equation of each of the circles that satisfies the stated conditions. In some cases there may be more than one circle that satisfies the conditio ns. Express the final equations in the form \(x^{2}+y^{2}+D x+E y+F=0\). $$ \text { Center at }(-3,4) \text { and } r=2 \quad x^{2}+y^{2}+6 x-8 y+21=0 $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}=-12 y $$

For Problems 1-14, write the equation of each of the circles that satisfies the stated conditions. In some cases there may be more than one circle that satisfies the conditions. Express the final equations in the form \(x^{2}+y^{2}+D x+E y+F=0\). Center at \((-1,-5)\) and \(r=3\) \(x^{2}+y^{2}+2 x+10 y+17=0\)

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ \frac{x^{2}}{4}+\frac{y^{2}}{16}=1 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}=8 y $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 9 x^{2}+3 y^{2}=27 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ y^{2}=-2 x $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 4 x^{2}+3 y^{2}=36 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ y^{2}=6 x $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 2 x^{2}+5 y^{2}=50 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}=6 y $$

For Problems 1-14, write the equation of each of the circles that satisfies the stated conditions. In some cases there may be more than one circle that satisfies the conditions. Express the final equations in the form \(x^{2}+y^{2}+D x+E y+F=0\). Center at the origin and \(r=7\) $$ x^{2}+y^{2}-49=0 $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 2 x^{2}+5 y^{2}=50 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}=-7 y $$

For Problems 1-14, write the equation of each of the circles that satisfies the stated conditions. In some cases there may be more than one circle that satisfies the conditions. Express the final equations in the form \(x^{2}+y^{2}+D x+E y+F=0\). $$ \text { Center at the origin and } r=1 \quad x^{2}+y^{2}-1=0 $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 12 x^{2}+y^{2}=36 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}=12(y+1) $$

For Problems 1-14, write the equation of each of the circles that satisfies the stated conditions. In some cases there may be more than one circle that satisfies the conditions. Express the final equations in the form \(x^{2}+y^{2}+D x+E y+F=0\). Tangent to the \(x\) axis, a radius of length 4 , and abscissa of center is \(-3 \quad x^{2}+y^{2}+6 x-8 y+9=0\) and \(x^{2}+y^{2}+6 x+8 y+9=0\)

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 8 x^{2}+y^{2}=16 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}=-12(y-2) $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 7 x^{2}+11 y^{2}=77 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ y^{2}=-8(x-3) $$

For Problems 1-14, write the equation of each of the circles that satisfies the stated conditions. In some cases there may be more than one circle that satisfies the conditions. Express the final equations in the form \(x^{2}+y^{2}+D x+E y+F=0\). Tangent to both axes, a radius of 6 , and the center in the third quadrant $$ x^{2}+y^{2}+12 x+12 y+36=0 $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 4 x^{2}+y^{2}=12 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ y^{2}=4(x+1) $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ \frac{(x-2)^{2}}{9}+\frac{(y-1)^{2}}{4}=1 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}-4 y+8=0 $$

For Problems 1-14, write the equation of each of the circles that satisfies the stated conditions. In some cases there may be more than one circle that satisfies the conditions. Express the final equations in the form \(x^{2}+y^{2}+D x+E y+F=0\). Tangent to the \(y\) axis, \(x\) intercepts of 2 and 6 See below

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ \frac{(x+3)^{2}}{16}+\frac{(y-2)^{2}}{4}=1 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}-8 y-24=0 $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ (x-5)^{2}+(y-7)^{2}=25 $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ \frac{(x+1)^{2}}{9}+\frac{(y+2)^{2}}{16}=1 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}+8 y+16=0 $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ \frac{(x-4)^{2}}{4}+\frac{(y+2)^{2}}{25}=1 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}+4 y-4=0 $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ (x+6)^{2}+(y-9)^{2}=49 $$ \((-6,9) ; r=7\)

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 4 x^{2}-8 x+9 y^{2}-36 y+4=0 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ y^{2}-12 x+24=0 $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ (x+1)^{2}+(y+8)^{2}=12 \quad(-1,-8) ; r=2 \sqrt{3} $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ x^{2}+6 x+9 y^{2}-36 y+36=0 $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ (x-7)^{2}+(y+2)^{2}=24 \quad(7,-2) ; r=2 \sqrt{6} $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 4 x^{2}+16 x+y^{2}+2 y+1=0 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ (x-2)^{2}=-4(y+2) $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ 3(x-10)^{2}+3(y+5)^{2}=9 \quad(10,-5) ; r=\sqrt{3} $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ (x+3)^{2}=4(y-4) $$