91Ó°ÊÓ

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

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ x^{2}+y^{2}+10 x+14 y+73=0 \quad(-5,-7), r=1 $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ x^{2}+6 x+8 y+1=0 $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 2 x^{2}+12 x+11 y^{2}-88 y+172=0 $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ x^{2}+y^{2}+7 x-2=0 \quad\left(-\frac{7}{2}, 0\right) ; r=\frac{\sqrt{57}}{2} $$

Find the vertices, the endpoints of the minor axis, and the foci of the given ellipse, and sketch its graph. See answer section. $$ 9 x^{2}+72 x+y^{2}+6 y+135=0 $$

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

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ y^{2}-2 y+12 x-35=0 $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ x^{2}+y^{2}-5 y-1=0 \quad\left(0, \frac{5}{2}\right): r=\frac{\sqrt{29}}{2} $$

Find an equation of the ellipse that satisfies the oiven conditions. Vertices \((\pm 4,0)\), foci \((\pm 2,0) \quad 3 x^{2}+4 y^{2}=48\)