91Ó°ÊÓ

Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. $$ 4 x^{2}+y^{2}=16 $$

(a) Use the identification theorem (12.14) to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a suitable rotation of axes to find an equation for the granh in an \(x^{\prime} y^{\prime}\) -plane, and sketch the graph, labeling vertices. $$ 5 x^{2}-8 x y+5 y^{2}=9 $$

Exer \(1-16\) : Find the vertices and foci of the conic, and sketch its graph. $$ 9 y^{2}=144-16 x^{2} $$

Find the vertices and foci of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$ \frac{x^{2}}{49}-\frac{y^{2}}{16}=1 $$

Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. $$ y^{2}+9 x^{2}=9 $$

Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$ x^{2}=-3 y $$

Exer \(1-16\) : Find the vertices and foci of the conic, and sketch its graph. $$ 9 y^{2}=144+16 x^{2} $$

(a) Use the identification theorem (12.14) to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a suitable rotation of axes to find an equation for the granh in an \(x^{\prime} y^{\prime}\) -plane, and sketch the graph, labeling vertices. $$ 11 x^{2}+10 \sqrt{3} x y+y^{2}=4 $$

Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix. $$ y=8 x^{2} $$

Find the vertices and foci of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$ y^{2}-4 x^{2}=16 $$