91Ó°ÊÓ

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

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ x^{2}+y^{2}-4 x+2 y=0 \quad(2,-1), r=\sqrt{5} $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ x^{2}+y^{2}=8 \quad(0,0), r=2 \sqrt{2} $$

For Problems \(1-30\), find the vertex, focus, and directrix of the given parabola and sketch its graph. $$ y^{2}-6 y-12 x+21=0 $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. $$ 4 x^{2}+4 y^{2}=1 \quad(0,0), r=\frac{1}{2} $$

For Problems \(31-50\), find an equation of the parabola that satisfies the given conditions. $$ \text { Focus }\left(0,-\frac{1}{2}\right) \text {, directrix } y=\frac{1}{2} \quad x^{2}=-2 y $$

Find an equation of the ellipse that satisfies the oiven conditions. Vertices \((0, \pm 5)\), length of minor axis is 4 $$ 25 x^{2}+4 y^{2}=100 $$

For Problems \(31-50\), find an equation of the parabola that satisfies the given conditions. $$ \text { Focus }(-1,0) \text {, directrix } x=1 \quad y^{2}=-4 x $$

For Problems \(15-32\), find the center and the length of a radius of each of the circles. Find the equation of the line that is tangent to the circle \(x^{2}+y^{2}-2 x+3 y-12=0\) at the point \((4,1)\) \(6 x+5 y=29\)

For Problems \(15-32\), find the center and the length of a radius of each of the circles. Find the equation of the line that is tangent to the circle \(x^{2}+y^{2}+4 x-6 y-4=0\) \(x-4 y=3\) at the point \((-1,-1)\)