91Ó°ÊÓ

convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes. $$ 9 x^{2}-16 y^{2}-36 x-64 y+116=0 $$

Identify the conic and graph the equation: $$ r=\frac{4 \sec \theta}{2 \sec \theta-1} $$

graph each relation. Use the relation’s graph to determine its domain and range. $$ \frac{x^{2}}{9}-\frac{y^{2}}{16}=1 $$

In Exercises 49–56, identify each equation without completing the square. $$ 4 x^{2}-9 y^{2}-8 x-36 y-68=0 $$

In Exercises \(51-60,\) convert each equation to standard form by completing the square on \(x\) and \(y .\) Then graph the ellipse and give the location of its foci. $$ 9 x^{2}+25 y^{2}-36 x+50 y-164=0 $$

Write a polar equation of the conic that is named and described. Ellipse: a focus at the pole; vertex: \((4,0) ; e=\frac{1}{2}\)

Use a graphing utility to graph each equation. $$7 x^{2}+6 x y+2.5 y^{2}-14 x+4 y+9=0$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed \(2 x^{2}-3 y^{2}+6 y+4=0\) by using the procedure for writing the equation of a rotated conic in standard form.

graph each relation. Use the relation’s graph to determine its domain and range. $$ \frac{x^{2}}{25}-\frac{y^{2}}{4}=1 $$

In Exercises 49–56, identify each equation without completing the square. $$ 9 x^{2}+25 y^{2}-54 x-200 y+256=0 $$