91Ó°ÊÓ

Exercises \(53-56\) give equations for hyperbolas and tell how many units up or down and to the right or left each hyperbola is to be shifted. Find an equation for the new hyperbola, and find the new center, foci, vertices, and asymptotes. $$ \frac{x^{2}}{16}-\frac{y^{2}}{9}=1, \quad \text { left } 2, \text { down } 1 $$

Replace the Cartesian equations in Exercises \(49-62\) by equivalent polar equations. $$ x^{2}-y^{2}=1 $$

Graph the lines and conic sections in Exercises \(47-56\) $$ r=1 /(1+\cos \theta) $$

Graph the lines and conic sections in Exercises \(47-56\) $$ r=1 /(1+2 \sin \theta) $$

Exercises \(53-56\) give equations for hyperbolas and tell how many units up or down and to the right or left each hyperbola is to be shifted. Find an equation for the new hyperbola, and find the new center, foci, vertices, and asymptotes. $$ y^{2}-x^{2}=1, \quad \text { left } 1, \text { down } 1 $$

Replace the Cartesian equations in Exercises \(49-62\) by equivalent polar equations. $$ \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 $$

Replace the Cartesian equations in Exercises \(49-62\) by equivalent polar equations. $$ x y=2 $$

Exercises \(53-56\) give equations for hyperbolas and tell how many units up or down and to the right or left each hyperbola is to be shifted. Find an equation for the new hyperbola, and find the new center, foci, vertices, and asymptotes. $$ \frac{y^{2}}{3}-x^{2}=1, \quad \text { right } 1, \text { up } 3 $$

Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in Exercises \(57-68 .\) $$ x^{2}+4 x+y^{2}=12 $$

Replace the Cartesian equations in Exercises \(49-62\) by equivalent polar equations. $$ x^{2}+x y+y^{2}=1 $$